If $A$ and $B$ are square matrices of the same order,then which of the following properties holds true?

If $A = \begin{bmatrix} 1 & -2 \\ 4 & 5 \end{bmatrix}$ and $f(t) = t^2 - 3t + 7$, then $f(A) + \begin{bmatrix} 3 & 6 \\ -12 & -9 \end{bmatrix}$ is equal to

If the matrix product $AB = O$,where $O$ is the null matrix,then which of the following is necessarily true?

Let $\alpha, \beta, \gamma$ be real numbers. If $\begin{bmatrix} 7 & 5 & \alpha \\ \beta & 2 & 11 \\ 3 & \gamma & 1 \end{bmatrix} \begin{bmatrix} 1 \\ 3 \\ 2 \end{bmatrix} = \begin{bmatrix} \alpha+\beta \\ -2\alpha+\beta-2\gamma \\ \alpha+2\beta+3\gamma \end{bmatrix}$, then find the value of $100+\frac{2\alpha+11\beta}{\gamma}$.

If $A=\left[\begin{array}{lll}9 & 3 & 0 \\ 1 & 5 & 8 \\ 7 & 6 & 2\end{array}\right]$ and $AA^T-A^2=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]$, then $\sum_{\substack{1 \leq i \leq 3 \\ 1 \leq j \leq 3}} a_{i j}=$

If $ 2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $,then the values of $ x $ and $ y $ are: