Question

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$, then compute $A^2 - 4A - 5I$.

Hint:

Notice the highly symmetric structure of matrix $A$. Because it is a symmetric matrix where all diagonal values are identical and all off-diagonal values are identical, its square $A^2$ preserves this exact pattern. This helps verify your arithmetic symmetry quickly.

Answer 1