Let $A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$ and $B$ be two matrices such that $A^{100} = 100B + I$. Then the sum of all the elements of $B^{100}$ is _______

The number of $3 \times 2$ matrices A , which can be formed using the elements of the set $\{-2,-1,0,1,2\}$ such that the sum of all the diagonal elements of $\mathrm{A}^{\mathrm{T}} \mathrm{A}$ is 5 , is

$\_\_\_\_$

Let $A=\left[\begin{array}{ccc}0 & 2 & -3 \\ -2 & 0 & 1 \\ 3 & -1 & 0\end{array}\right]$ and $B$ be a matrix such that $B(I-A)=I+A$. Then the sum of the diagonal elements of $\mathrm{B}^{\mathrm{T}} \mathrm{B}$ is equal to $\_\_\_\_$

Let $|\mathrm{A}|=6$, where A is a $3 \times 3$ matrix. If $\left|\operatorname{adj}\left(3\operatorname{adj}\left(\mathrm{A}^2 \cdot \operatorname{adj}(2 \mathrm{~A})\right)\right)\right|=2^{\mathrm{m}} \cdot 3^{\mathrm{n}}, \mathrm{m}, \mathrm{n} \in \mathbf{N}$, then $\mathrm{m}+\mathrm{n}$ is equal to

$\_\_\_\_$ .