If A = \begin{pmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{pmatrix}, then A^2 - 4A - 5I is equal to
Step-by-Step Solution
Key Concept: Calculate A^2, then substitute into the expression A^2 - 4A - 5I to see if it results in the zero matrix.
First, calculate A^2 = A * A. Then compute 4A and 5I. Finally, perform the matrix subtraction A^2 - 4A - 5I. The result is the zero matrix O.
Correct Answer: 1