Find A3
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 A3
\[ A^3 = (-I)^3 = (-1)^3 I^3 \]
\[ A^3 = -1 \cdot I = -I \]
Final Answer:
\[ A^3 = \begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{bmatrix} \]