If $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$ and $AB = O$,then $B =$

If $A = \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}$,then $A^n = \begin{bmatrix} 1 & 0 \\ n & 1 \end{bmatrix}$ for all $n \in N$. Which of the following is correct?

Let $G(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}$. If $x+y=0$,then $G(x) G(y) =$

If $A = \begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$,then $A^4$ is equal to

If $A = \begin{bmatrix} 3 & \sqrt{3} & 2 \\ 4 & 2 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & -1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$,verify that $(kB)^{\prime} = kB^{\prime}$,where $k$ is any constant.

Let $A=\begin{bmatrix} a & 3 & 5 \\ 5 & -1 & 3 \\ 2 & 3 & -4 \end{bmatrix}$ and $B=\begin{bmatrix} b & 1 & 4 \\ 4 & c & 1 \\ -3 & 1 & d \end{bmatrix}$. If the trace of $A$ is $-4$ and $AB=\begin{bmatrix} -1 & 0 & 17 \\ -3 & 10 & 25 \\ 28 & -8 & 3 \end{bmatrix}$, then $a+b+c+d=$