Matrices Test -...

If $$\begin{bmatrix} \alpha  & \beta  \\ \gamma  & -\alpha  \end{bmatrix}$$ to the square is two rowed unit matrix, then $$\alpha ,\beta ,\gamma $$ should satisfy the relation

If $$A=\begin{bmatrix} 1 & -3 \\ 2 & k \end{bmatrix}$$ and $${ A }^{ 2 }-4A+10I=A$$, then $$k$$ is equal to

If $$A=\begin{bmatrix} \alpha  & 0 \\ 1 & 1 \end{bmatrix}$$ and $$B=\begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}$$, then value of $$\alpha$$ for which $${A}^{2}=B$$, is

If $$A = \begin{bmatrix}1 &3 \\ 3 & 4\end{bmatrix}$$ and $$A^{2} - kA - 5I_{2} = 0$$, then the value of $$k$$ is

If $$A$$ is a non zero square matrix of order $$n$$ with $$det\left( I+A \right) \neq 0$$, and $${A}^{3}=0$$, where $$I,O$$ are unit and null matrices of order $$n\times n$$ respectively, then $${ \left( I+A \right)  }^{ -1 }=$$

If $$\quad A=\begin{pmatrix} 1 & 3 \\ 4 & 5 \end{pmatrix}$$ then $${ A }^{ -1 }$$ equals

If $$A = \begin{bmatrix} 1& 4 & 4\\ 4 & 1 & 4\\ 4 & 4 & 1\end{bmatrix}$$, then $$A^{2} - 6A =$$ _____.

If $$A = \begin{bmatrix} 2& 3\\ -1 & 2\end{bmatrix}$$, then $$A^{3} + 3A^{2} - 4A + 1$$ is equal to

If $$A=\begin{bmatrix} 0 & 0 \\ 0 & 5 \end{bmatrix}$$, then $${ A }^{ 12 }$$ is

If $$A=\begin{pmatrix} 3 & 1 \\ -9 & -3 \end{pmatrix}$$ then $${ \left( 1+2A+3{ A }^{ 2 }+....\infty  \right)  }^{ -1 }$$ equals