If $A=\begin{bmatrix} 1 & 1 & 1 \ 1 & 1 & 1 \ 1 & 1 & 1 \end{bmatrix}$ then $A^n=\begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \ 3^{n-1} & 3^{n-1} & 3^{n-1} \ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix}$ , $n \in N$

If $A = \begin{bmatrix}1\ 2\ 3
\end{bmatrix}$ then $AA^{1}$.

If for the matrix $A.A^3=1$, then $A^{-1}=$

Let $A$ be a square matrix such that $A^2 = A$ and $|A| \neq 0$, then choose the correct option.

For two matrices $A$ and $B$, if $AB=0$, then

For any non-singular matrix A, $ \displaystyle A^{-1} $ =

If $A=\begin{bmatrix} \cos { \alpha  }  & -\sin { \alpha  }  \ \sin { \alpha  }  & \cos { \alpha  }  \end{bmatrix}$, $B=\begin{bmatrix} \cos { 2\beta  }  & \sin { 2\beta  }  \ \sin { 2\beta  }  & -\cos { 2\beta  }  \end{bmatrix}$, where 0 < $\beta$ < ${ \pi  }/{ 2 }$, then prove that $BAB=$ ${ A }^{ -1 }$.

Let $A$ be a $3\times 2$ matrix with real entries. Let $H = A(A^{T}A)^{-1}A^{T}$ where $A^{T}$ is the transpose of $A$ and let $I$ be the identity matrix of order $3\times 3$. Then

If $A^3 = 0$ then $1 + A + A^2$ is equal to

Find the number of all possible ordered sets of two $(n\times n)$ matrices A and B for which $AB-BA=$$I$.

If $\omega$ is the complex cube root of unity, then inverse of $\begin{bmatrix} \omega  & 0 & 0 \ 0 & { \omega  }^{ 2 } & 0 \ 0 & 0 & { \omega  }^{ 2 } \end{bmatrix}$ is

The inverse of the matrix $\begin{bmatrix}1 & 0 & 1\ 0 & 2 & 3\ 1 & 2& 1\end{bmatrix}$ is

If A =$\left[ \begin{matrix} i \ 0 \end{matrix}\begin{matrix} 0 \ -1 \end{matrix} \right] $, than check whether: ${{\text{A}}^2} =  - {\text{I,(}}{{\text{i}}^2} =  - 1)$

If $A = \left[ \begin{array}{l}\cos \theta \,\,\,\,\sin \theta \ - \sin \theta \,\,\,\cos \theta \end{array} \right]$ where $\theta  = \frac{{2\pi }}{{19}}$ then ${A^{2017}} = $

If A and B are matrices of the same order, then $\displaystyle :\left ( A+B \right )^{2}= A^{2}+2AB+B^{2}$ is possible, iff

If $A$ and $B$ are any two matices, then  

If $A^{2}-A+I=0$, then inverse of $A$ is

The matrices $\begin{bmatrix} \cos { \theta  }  & -\sin { \theta  }  \ \sin { \theta  }  & \cos { \theta  }  \end{bmatrix}$ and $\begin{bmatrix} a & 0 \ 0 & b \end{bmatrix}$ commute under multiplication

If $A$ and $B$ are two square matrices of order $3 \times  3$ which satisfy $AB = A$ and $BA = B$, then Which of the following is true?

The multiplication of matrices is distributive with respect to the matrix addition.

The inverse of the matrix $\begin{bmatrix}3 & 5 & 7 \ 2 & -3 & 1 \ 1 & 1 & 2\end{bmatrix}$ is $\begin{bmatrix}7 & -3 & 26 \ 3 & 1 & 11 \ -5 & -2 & 0\end{bmatrix}$.
State true or false.

 In matrices $AB = O$ does not necessarily mean that 

If inverse of $A=\left[ \begin{matrix} 1 & 1 & 1 \ 2 & -1 & -1 \ 1 & -1 & 1 \end{matrix} \right] $ is $\cfrac { -1 }{ 6 } \left[ \begin{matrix} -2 & -2 & 0 \ -3 & 0 & \alpha  \ -1 & 2 & -3 \end{matrix} \right] $ then $\alpha=$

Let $\displaystyle A=\begin{pmatrix}1 &2 \3  &4
\end{pmatrix}$ and $\displaystyle B=\begin{pmatrix}a &0 \0  &b \end{pmatrix} a,b \epsilon N.$Then

If $A$ is an invertible square matrix then $|A^{-1}| = ?$

If $A = \begin{bmatrix} -2& 3\ 1 & 1\end{bmatrix}$ then $|A^{-1}| = ?$

If matrices $A$ and $B$ anticommute then

Let $A$ and $B$ be two $2 \times 2$ matrices. Consider the statements
          $(i)$ $AB =0 \Rightarrow A = 0 :or :B = 0$
         $ (ii)$ $AB =I \Rightarrow A =B^{-1}$
          $(iii)$ $(A + B)^2 = A^2 + 2AB + B^2$

If $A = \begin{bmatrix} 2& -1\ 1 & 3\end{bmatrix}$, then $A^{-1} = ?$

If $A$ and $B$ are invertible square matrices of the same order then $(AB)^{-1} = ?$

If $A$ and $B$ are two square matrices of the same order and $m$ is a positive integer, then
$(A + B)^m =$ $^mC _0A^m +$ $^mC _1 A^{m -1} B + ^mC _2A^{m-2} B^2 + ... +$ $^mC _{m- 1} AB^{m-1}+$ $^mC _m B^m$ if

Let $A, : B : and : C$ be $2\times 2$ matrices with entries from the set of real numbers. Define $\ast $ as follows: $\displaystyle A\ast B=\frac{1}{2}(AB + BA)$, then

If $A$ and $B$ are square matrices of the same order such that $A^2=A,:B^2=B, :AB = BA = 0$, then

If $A^k=0$ for some value of $k$ and $B=1+A+A^2+...+A^{k-1},$ then $B^{-1}$ equal

Let $A, : B : and : C$ be $2\times 2$ matrices with entries from the set of real numbers. Define $\ast $ as follows:
  $\displaystyle A \ast B=\frac{1}{2}(AB\,'+A'B)$. Which of the given is true?

Say true or false:

If $A$ is a non-singular matrix, then 

The inverse of a skew-symmetric matrix of an odd order is

If $AB=A$ and $BA=B$, where $A$ and $B$ are square matrices, then 

If $A=\begin{bmatrix} 0 & 1 \ 1 & 0 \end{bmatrix}$, $B=\begin{bmatrix} 0 & -i \ i & 0 \end{bmatrix}$ then ${(A+B)}^{2}$ equals

If $D=diag({d} _{1}, {d} _{2}, {d} _{3}........{d} _{n})$, where ${d} _{1}\ne 0$ for all $i=1, 2,.....n$, then ${D}^{-1}$ is equal to

If for suitable matrices $A, B$; $AB=A$ and $BA=B$; then ${A}^{2}$ equals-

lf $\mathrm{A}$ is $\left{\begin{array}{lll}
8 & -6 & 2\
-6 & 7 & -4\
2 & -4 & \lambda
\end{array}\right}$  is a singular matrix then  $\lambda =$ 

If $\left[\begin{array}{ll}
\mathrm{x} & \mathrm{y}^{3}\
2 & 0
\end{array}\right]=\left[\begin{array}{ll}
1 & 8\
2 & 0
\end{array}\right]$, then  $\left[\begin{array}{ll}
\mathrm{x} & \mathrm{y}\
2 & 0
\end{array}\right]^{-1}$ is equal to

$p=$ $\begin{bmatrix}
0 & x &0 \
 0& 0 & 1
\end{bmatrix}$, then $p^{-1}$=

A= $\begin{bmatrix}
cos\alpha  & -sin\alpha \
sin\alpha  & cos\alpha
\end{bmatrix}$ ,then find which of the following are correct 
I) A is singular matrix
II) $A^{-1}$=$A^{T}$
III) A is symmetric matrix
IV) $A^{-1}= -A$

If AB=KI where $\displaystyle K\in R$ then $\displaystyle A^{-1}$= _____

If A=$\displaystyle \begin{vmatrix} 5 & -3   \ 4 & 2   \end{vmatrix}$ then find $\displaystyle AA^{-1}$

If $\displaystyle A=\left[ \begin{matrix} \cos { \theta  }  & \sin { \theta  }  \ -\sin { \theta  }  & \cos { \theta  }  \end{matrix} \right] $, then $\displaystyle \underset { n\rightarrow \infty  }{ \lim } \frac { 1 }{ n } { A }^{ n }$ is?

If A is invertible, then which of the following is not true?

Which of the following matrices is not invertible?

If the matrix $\displaystyle \left[ \begin{matrix} a \ c \end{matrix}\begin{matrix} b \ d \end{matrix} \right] $ is commutative with the matrix $\displaystyle \left[ \begin{matrix} 1 \ 0 \end{matrix}\begin{matrix} 1 \ 1 \end{matrix} \right] $, then

Consider two matrix $A = \begin{bmatrix} 1 & 2\ 2 & 1\ 1 & 1 \end{bmatrix}$ and $ B = \begin{bmatrix} 1 & 2 & -4\  2 & 1 & -4 \end{bmatrix}$. Which one of the following is correct ?

If $A$ is a square matrix of order $3$ and det $A = 5$, then what is det $[(2A)^{-1}]$ equal to?

If A is a square matrix such that $A^2 = I $ where I is the identity matrix, then what is $A^{-1}$ equal to ?

If A is an orthogonal matrix of order 3 and $B=\begin{bmatrix}1&2&3\-3&0&2\2&5&0\end{bmatrix}$, then which of the following is/are correct?
1. $|AB|= \pm 47$
2. $AB=BA$
Select the correct answer using the code given below :

If A is a non singular matrix satisfying $A=AB-BA$, then which one of the following holds true

If A is a square matrix of order 3,then $|Adj\left( Adj{ A }^{ 2 } \right) |=$

If $AB=0$ for the matrices
$A=\left[ \begin{matrix} \cos ^{ 2 }{ \theta  }  & \cos { \theta  } \sin { \theta  }  \ \cos { \theta  } \sin { \theta  }  & \sin ^{ 2 }{ \theta  }  \end{matrix} \right] $ and $B=\left[ \begin{matrix} \cos ^{ 2 }{ \phi  }  & \cos { \phi  } \sin { \phi  }  \ \cos { \phi  } \sin { \phi  }  & \sin ^{ 2 }{ \phi  }  \end{matrix} \right] $ then $\theta-\phi $ is

Let $A$ and $B$ are two matrices such that $AB =BA$, then for every $n\in N$,

If $D _1$ and $D _2$ are two $3\times 3$ diagonal matrices, then

if $\begin{bmatrix}2 &1 \ 7 &4 \end{bmatrix}$A$\begin{bmatrix}-3 &2 \ 5 &-3 \end{bmatrix}=\begin{bmatrix}1 &0 \ 0&1 \end{bmatrix}$, then matrix A equals

Lets $A=\begin{bmatrix} 0&5 \-5 & 0\end{bmatrix}$ be a skew symmetric matrix and $I + A$ is non singular, then the matrix $B = (I - A)(I + A)^{-1}$ is