If then A6 = ____________

Engineering

Mathematics

Introduction to Matrix

Special Type of Square Matrices

Question

If $A = [\begin{array}{lll} 2 0 0 \\ 0 2 0 \\ 0 0 2 \end{array}]$ then A⁶ = _____________.

16A

12A

32A

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A = [\begin{array}{lll} 2 0 0 \\ 0 2 0 \\ 0 0 2 \end{array}] = 2 [\begin{array}{lll} 1 0 0 \\ 0 1 0 \\ 0 0 1 \end{array}] = 2 I

∴ A⁶ = (2I)⁶ = 2⁶ × I⁶ = 2⁶I
A⁶ = 2⁶I = 2⁵(2I) = 2⁵A = 32 A