If $ A = \left[\begin{array}{cc} 3 & 1 \\2 & 4 \end{array}\right] $, then the determinant of the adjoint of $ A^2 $ is:
100
Let \( A = \begin{bmatrix} \alpha & -1 \\6 & \beta \end{bmatrix},\ \alpha > 0 \), such that \( \det(A) = 0 \) and \( \alpha + \beta = 1 \). If \( I \) denotes the \( 2 \times 2 \) identity matrix, then the matrix \( (1 + A)^5 \) is: