If $A = \begin{bmatrix}4 & -3 \\ 2 & -1\end{bmatrix}$ and $A^2 = kA - 2I$, what is $k$?

Explanation

1. 01

   $A^2 = \begin{bmatrix}10 & -9 \\ 6 & -5\end{bmatrix}$.

2. 02

   Compare the top-left elements of $A^2 = kA - 2I$: $10 = 4k - 2$, so $k = 3$; the other elements agree.