Find A4
Given:
\[ A = \begin{bmatrix} -3 & 0 \\ 0 & -3 \end{bmatrix} \]
Step 1: Recognize the Matrix
\[ A = -3I \]
Step 2: Compute A4
\[ A^4 = (-3I)^4 = (-3)^4 I^4 \]
\[ A^4 = 81I \]
Final Answer:
\[ A^4 = \begin{bmatrix} 81 & 0 \\ 0 & 81 \end{bmatrix} \]