$A$ square matrix $[a_{ij}]_{n \times n}$ is an upper triangular matrix if:

If $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -3 \end{bmatrix}$, then $A^2 + B^2=$ . . . . . . .

If $\begin{bmatrix} 2 & -3 \\ 4 & 0 \end{bmatrix} - \begin{bmatrix} a & c \\ b & d \end{bmatrix} = \begin{bmatrix} 1 & 4 \\ 2 & -5 \end{bmatrix}$,then $(a, b, c, d) = $

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

For matrices $A$ and $B$,$A^{\prime} = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ and $B^{\prime} = \begin{bmatrix} 4 & 3 & 2 \end{bmatrix}$,then $(BA)^{\prime}$ is . . . . . . .

Let $A = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 1 & -1 \\ 0 & 0 & 1 \end{bmatrix}$ and $B = 7A^{20} - 20A^{7} + 2I$,where $I$ is an identity matrix of order $3 \times 3$. If $B = [b_{ij}]$,then $b_{13}$ is equal to $....$