$A = \left[ {\begin{array}{*{20}{c}}1&0\\1&1\end{array}} \right]$ and $I = \left[ {\begin{array}{*{20}{c}}
1&0\\0&1\end{array}} \right]$ , then which of the following holds for all $n \geq 2, n \in N$ ?

Let $A=\left[a_{i j}\right]$ be a real matrix of order $3 \times  3$, such that $a_{i 1}+a_{i 2}+a_{i 3}=1$, for $i=1,2,3$. Then, the sum of all the entries of the matrix $A^{3}$ is equal to:

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

For how many value $(s)$ of $x$ in the closed interval $[ – 4,\,\, – 1]$ is the matrix $\left[ {\begin{array}{*{20}{c}}3&{ – 1 + x}&2\\3&{ – 1}&{x + 2}\\{x + 3}&{ – 1}&2\end{array}} \right]$  singular

If $\quad A=\left[\begin{array}{rrr}1 & 1 & -1 \\ 2 & 0 & 3 \\ 3 & -1 & 2\end{array}\right]$,  $B=\left[\begin{array}{rr}1 & 3 \\ 0 & 2 \\ -1 & 4\end{array}\right]$ and $C=\left[\begin{array}{rrrr}1 & 2 & 3 & -4 \\ 2 & 0 & -2 & 1\end{array}\right],$ find $A(B C),(A B) C$ and show that $(A B) C=A(B C)$.