If `A=[(2 ,0 ,0),( 0 ,2 ,0),( 0 ,0 ,2)]` , then `A^5=`
(a) `5A` (b) `10 A` (c) `16 A` (d) `32 A`

Explanation

To find \( A^5 \) for the matrix \( A = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{pmatrix} \), we can use the property of powers of a diagonal matrix.

### Step 1: Calculate \( A^2 \)

\[ A^2 = A \times A = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{pmatrix} \times \begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{pmatrix} \]

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