List of top Engineering Mathematics Questions on Matrix Operations asked in GATE BM

If the given matrices \[ A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix}, \quad I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \] satisfy \( A^{2} = kA - 2I\), \(\text{ the value of coefficient }\) k \(\text{ is}\) _________.