If $A$ is a square matrix such that $A^2 = A$,then $(I + A)^2 - 3A =$ . . . . . . .

If $A = \begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$,then $A^n$ (where $n \in N$) equals

If $A$ and $B$ are two matrices such that $A+B$ and $AB$ are both defined, then

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation $A A^T = 9 I$,where $I$ is the identity matrix,then $a^2 + b^2 =$

If $A = \begin{bmatrix} 1 & 2 & -1 \\ 3 & 0 & 2 \\ 4 & 5 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 0 & 1 & 3 \end{bmatrix}$,then $AB$ is:

Let $A = \begin{bmatrix} 0 & 1 \\ 1 & k \end{bmatrix}$, $k \in R$ and $A^3 = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$. If $d = 228$, then $b + c =$