Matrices Test -...

If $$A=\begin{bmatrix} 4 & -1 \\ -1 & k \end{bmatrix}$$ such that $$A^{2}-6A+7I=0$$, then $$k=$$

If $$A\begin{bmatrix} 1 & 1\\ 2 & 0\end{bmatrix}=\begin{bmatrix} 3 & 2\\ 1 & 1\end{bmatrix}$$, then $$A^{-1}$$ is given by?

A is an involuntary matrix given by $$A=\begin{bmatrix} 0 & 1 & -1\\ 4 & -3 & 4\\ 3 & -3 & 4\end{bmatrix}$$ then the inverse of $$\dfrac{A}{2}$$ will be?

A is an involutory matrix given by $$A=\begin{bmatrix} 0 & 1 & -1 \\ 4 & -3 & 4 \\ 3 & -3 & 4 \end{bmatrix}$$ then the inverse of $$\dfrac{A}{2}$$ will be 

Let A=$$\left[ \begin{matrix} 1 \\ 2 \end{matrix}\begin{matrix} 2 \\ 1 \end{matrix} \right] and\quad B=\left[ \begin{matrix} 4 \\ 5 \\ 0 \end{matrix}\begin{matrix} -3 \\ 6 \\ 1 \end{matrix} \right] $$ then

If $$\left[ \begin{matrix} 1 & x & 1 \end{matrix} \right] \left[ \begin{matrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2 \end{matrix} \right] \left[ \begin{matrix} 1 \\ 1 \\ x \end{matrix} \right] =0,$$ then $$x=$$

if A=$$\left[ \begin{matrix} 2 & 3 \\ 5 & -7 \end{matrix} \right] then\quad \left( { A }^{ '} \right) ^{ 2 }=$$

If $$A$$ and $$B$$ are two matrices such that $$AB$$ and $$A+B$$ are both defined then $$A$$ and $$B$$ are 

If $$A=\left[ \begin{matrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{matrix} \right] $$, then value of $$A^{-1}$$ is equal to 

If $$U = [ 2, -3 , 4 ]$$ , $$V = \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix}$$ , $$X = [0 , 2 , 3]$$ and $$Y = \begin{bmatrix} 2 \\ 2 \\ 4 \end{bmatrix}$$ , then $$UV + XY$$ =