Find A2
Given:
\[ A = \begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{bmatrix} \]
Step 1: Recognize the Matrix
\[ A = -I \]
Step 2: Compute A2
\[ A^2 = (-I)^2 = (-1)^2 I^2 \]
\[ A^2 = 1 \cdot I = I \]
Final Answer:
\[ A^2 = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \]