​$$\text { Let } A=\left(\begin{array}{cc}\alpha & 1 \\0 & -1\end{array}\right) \text { and } B=\left(\begin{array}{ll}4 & 1 \\0 & 1\end{array}\right) \text {, such that } A^2=B \text {, then the value of } \alpha \text { is: }$$​​

​$$\text { Let } A=\left(\begin{array}{cc}\alpha & 1 \\0 & -1\end{array}\right) \text { and } B=\left(\begin{array}{ll}4 & 1 \\0 & 1\end{array}\right) \text {, such that } A^2=B \text {, then the value of } \alpha \text { is: }$$​​

​$$\text{If } A = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 4 & 5 \\ 5 & 6 & 7 \end{bmatrix} \text{ and } B = \begin{bmatrix} 1 & 1 & 1 \\ 2 & 2 & 2 \\ 3 & 3 & 3 \end{bmatrix}, \text{ then } \det(A + B) = ?$$​​

The product of the cofactors of 3 and -2 in the matrix $$\begin{bmatrix}1 & 0 & -2 \\3 & -1 & 2 \\4 & 5 & 6\end{bmatrix}$$​ is: