Matrices Test -...

If $$\displaystyle A=\left[ \begin{matrix} 2 \\ 0 \\ 0 \end{matrix}\,\,\,\begin{matrix} 0 \\ 2 \\ 0 \end{matrix}\,\,\,\begin{matrix} 0 \\ 0 \\ 2 \end{matrix} \right] $$ then $$\displaystyle { A }^{ 5 }=$$

If $$A$$ and $$B$$ are symmetric matrices, then $$ABA$$ is

If $$A=\begin{bmatrix}1 & 1\\ 1& 1\end{bmatrix}$$, then $$A^{100}$$ is equal to.

If $$\displaystyle A=\begin{bmatrix} 0 & 0 & 1\\ 0 & 1&0 \\ 1& 0 & 0\end{bmatrix}$$, then $$A^{-1}$$ is.

If $$A=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$, then $$A^2 - 5A$$ is equal to 

If $$\begin{bmatrix} 1 & 2 \\ 3 & -5 \end{bmatrix}$$, then $${A}^{-1}$$ is equal to

Inverse of the matrix $$\begin{bmatrix} \cos 2\theta & -\sin 2\theta\\ \sin 2\theta & \cos 2\theta\end{bmatrix}$$ is.

Let $$A=\begin{bmatrix} 1 & -1 & -1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}$$ and $$10B=\begin{bmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha  \\ 1 & -2 & 3 \end{bmatrix}$$, if $$B$$ is the inverse of matrix $$A$$, then $$\alpha $$ is

If $$\begin{bmatrix}1 & 1 &1\\ 1&-2 &-2\\1 & 3 &1\end{bmatrix}$$ $$\begin{bmatrix} x\\ y\\z\end{bmatrix}=\begin{bmatrix} 0 \\ 3\\4\end{bmatrix}$$, then $$\begin{bmatrix} x\\ y\\z\end{bmatrix}$$ is equal to.

If $$A=\begin{bmatrix} 1 & -2 & 1 \\ 2 & 1 & 3 \end{bmatrix}$$ and $$B=\begin{bmatrix} 2 & 1 \\ 3 & 2 \\ 1 & 1 \end{bmatrix}$$, then $${ \left( AB \right)  }^{ T }$$ is equal to