If $A = \left[ {\begin{array}{*{20}{c}}{ – 1}&0&0\\0&{ – 1}&0\\0&0&{ – 1}\end{array}} \right]$, then ${A^2}$is

The number of $3 \times 3$ non- singular matrices, with four entries as $1$ and all other entries as $0$, is 

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 $……..$.

Find the value of $x,\,y$ and $z$ from the following equation : $\left[\begin{array}{ll}x+y & 2 \\ 5+z & x y\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\end{array}\right]$

Let $2A+B = \left[ {\begin{array}{*{20}{c}}
  1&0&3 \\ 
  { – 1}&4&6 \\ 
  2&5&2 
\end{array}} \right],\,A – 2B = \left[ {\begin{array}{*{20}{c}}
  2&{ – 1}&5 \\ 
  0&3&6 \\ 
  1&2&1 
\end{array}} \right]$ . Then $Tr(A) -Tr(B)$ has the value equal to (where $Tr(A)$ denotes the trace of matrix $A$)