Compute the indicated products  $\left[\begin{array}{cc}a & b \\ -b & a\end{array}\right]\left[\begin{array}{lc}a & -b \\ b & a\end{array}\right]$

If $A = \left[ {\begin{array}{*{20}{c}}0&1\\0&0\end{array}} \right]$and $AB = O$, then $B =$

Let $P$ be a square matrix such that $P ^2= I – P$. For $\alpha, \beta, \gamma, \delta \in N$, if $P ^\alpha+ P ^\beta=\gamma I -29 P$ and $P ^\alpha- P ^\beta=$ $\delta I-13 P$, then $\alpha+\beta+\gamma-\delta$ is equal to $……..$.

Let $A=\left[\begin{array}{lll}0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0\end{array}\right]$, where $a, c \in R$. If $A^3=A$ and the positive value of a belongs to the interval ( $n -1, n$ ], where $n \in N$, then $n$ is equal to $……….$.

Let $A$ be a $2 \times 2$ matrix with $\operatorname{det}(A)=-1$ and det $(( A + I )(\operatorname{Adj}( A )+ I ))=4$. Then the sum of the diagonal elements of $A$ can be.