Matrices Test -...

If $$A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix}$$ and $$kA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}$$, then the value of $$k, a, b $$, are respectively. 

If $$A = \left[ {\begin{array}{*{20}{c}}2 & 0 & 0\\0 & 2 & 0\\0 & 0 & 2\end{array}} \right]$$ then $$A^6$$ = _____________.

If $$\left[ {\begin{array}{*{20}{c}}x & 4 & { - 1}\end{array}} \right]\left[ {\begin{array}{*{20}{c}}2 & 1 & 0\\1 & 0 & 2\\0 & 2 & 4\end{array}} \right]\left[ {\begin{array}{*{20}{c}}x\\4\\{ - 1}\end{array}} \right] = 0$$ then $$x$$ is equal to

If $$A=\begin{bmatrix} 0 & c & -b \\ -c & 0 & a \\ b & -a & 0 \end{bmatrix},B=\begin{bmatrix} { a }^{ 2 } & ab & ac \\ ba & { b }^{ 2 } & bc \\ ca & cb & { c }^{ 2 } \end{bmatrix}$$ then $$AB=$$ 

The value of $$x$$, so that $$\left\lceil 1\quad x\quad 1 \right\rceil \begin{bmatrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2 \end{bmatrix}\begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix}=0$$ is

If A be square matrix of order n and k is a scalar, then adj (KA) is:

If $$A = \left[ \begin{array} { c c } { a b } & { b ^ { 2 } } \\ { - a ^ { 2 } } & { - a b } \end{array} \right]$$ and $$A ^ { n } = 0$$ then the minimum value of $$n$$ is

If $$A$$ is matrix of order $$m\times n$$ and $$B$$ is a matrix such that $$AB'$$ and $$B'A$$ are both defined, then order of matrix $$B$$ is

If $$A=\left[ \begin{matrix} a & b \\ b & a \end{matrix} \right] $$ and $$A^{2}=\left[ \begin{matrix} \alpha  & \beta  \\ \beta  & \alpha  \end{matrix} \right] $$ then

If $$A = \left[ {\begin{array}{*{20}{c}}1&2\\3&4\end{array}} \right]$$, then $$8A^{-4}$$ is equal to