Matrices Test -...

If $$A=\begin{bmatrix} 2 & x-3 & x-2 \\ 3 & -2 & -1 \\ 4 & -1 & -5 \end{bmatrix}$$ is a symmetric matrices then $$x=$$

Given $$A$$ is a matrix of order $$3\times 2$$. If order of $$AB$$ is $$3\times 3$$, then order of $$B$$ will be 

Given $$A= \begin{bmatrix}  3&4  \\ 4&-3 \end{bmatrix}$$ and $$B = \begin{bmatrix} 24 \\ 7\end{bmatrix},$$ find the matrix $$X$$ such that $$AX=B$$.

The inverse of $$\begin{bmatrix} 1 & a & b \\ 0 & x & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ is $$\begin{bmatrix} 1 & -a & -b \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ then $$x=$$

If $$A = \left[ {\begin{array}{*{20}{c}}  2&{ - 3} \\   { - 4}&1 \end{array}} \right]$$, then $$\left[ {3{A^2} + 12A} \right]$$ is equal to 

$$A=\begin{bmatrix} a & b \\ 0 & c \end{bmatrix}$$ then $${A}^{-1}+(A-aI)(A-cI)=$$

If $$A=\begin{bmatrix} \cos { x }  & \sin { x }  \\ -\sin { x }  & \cos { x }  \end{bmatrix}$$ and $$A(AdjA)=k\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$ then the value of $$k$$ is

If $$A=\begin{bmatrix} 0 & a+1 & b-2 \\ 2a-1 & 0 & c-2 \\ 2b+1 & 2+c & 0 \end{bmatrix}$$ is skew symmetric then $$a+b+c$$=

If $$A$$ is square  matrix such that $${A^2} = 1$$ then $${A^{ - 1}} = ?$$

If $$A=\begin{bmatrix} 1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1 \end{bmatrix}$$ then $$A^ {2}$$ is equal to