If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}$,$I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $A^{2} = 8A + kI$,then the value of $k$ is

Simplify $\cos \theta \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix} + \sin \theta \begin{bmatrix} \sin \theta & -\cos \theta \\ \cos \theta & \sin \theta \end{bmatrix}$.

If $A=\begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix}$ and $B=\begin{bmatrix} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \end{bmatrix}$,then which one of the following is true?

If $R(t) = \begin{bmatrix} \cos t & \sin t \\ -\sin t & \cos t \end{bmatrix}$,then $R(s) \cdot R(t) = $

Let $A, B, C, D$ and $E$ be $n \times n$ matrices,each with non-zero determinant. If $ABCDE=I$,then $C^{-1}=$

If $A = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then the incorrect option among the following is