If then find A4.

Engineering

Mathematics

Introduction to Matrix

Special Type of Square Matrices

Question

If $A = [\begin{array}{lll} 3 0 0 \\ 0 3 0 \\ 0 0 3 \end{array}]$ then find A⁴.

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$A = [\begin{array}{lll} 3 0 0 \\ 0 3 0 \\ 0 0 3 \end{array}]$

$A = [\begin{array}{ccc} 3^{4} & 0 & 0 \\ 0 & 3^{4} & 0 \\ 0 & 0 & 3^{4} \end{array}] = [\begin{array}{ccc} 81 & 0 & 0 \\ 0 & 81 & 0 \\ 0 & 0 & 81 \end{array}]$