Let $M = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$ and $I$ be the identity matrix of order $3$. Then $M^2 - 4M =$

$A$ square matrix $[a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a

The number of all $3 \times 3$ matrices $A$,with entries from the set $\{-1, 0, 1\}$ such that the sum of the diagonal elements of $AA^{T}$ is $3$,is

The matrix $A = \frac{1}{3}\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ -2 & 2 & -1 \end{bmatrix}$ is

If $A=\begin{bmatrix} b & a & 0 \\ c & 0 & b \\ a & a & b \end{bmatrix}$ and $B=\begin{bmatrix} 0 & a & b \\ b & 0 & c \\ b & a & a \end{bmatrix}$ are two matrices such that $AB=\begin{bmatrix} 2 & 2 & 7 \\ 1 & 8 & 5 \\ 3 & 6 & 10 \end{bmatrix}$, then $a^2+b^2+c^2=$

Construct a $2 \times 2$ matrix,$A = [a_{ij}]$,whose elements are given by: $a_{ij} = \frac{(i+j)^2}{2}$