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

Let $A=\left[\begin{array}{lll}1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{array}\right], a, b \in R$. If for some $n \in N$, $A ^{ n }=\left[\begin{array}{ccc}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{array}\right]$ then $n + a + b$ is equal to $\dots\dots$

Let $\omega$ be a complex cube root of unity with $\omega \neq 1$ and $P=\left[p_j\right]$ be a $n \times n$ matrix with $p_{i j}=\omega^{i+j}$. Then $P ^2 \neq 0$, when $n =$

$(A)$ $57$ $(B)$ $55$ $(C)$ $58$ $(D)$ $56$

If $A = \left[ {\begin{array}{*{20}{c}}3&1\\{ – 1}&2\end{array}} \right]$, then ${A^2} = $

If $AB = C$, then matrices $A,B,C$are