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Choose the correct option.
If , then equals to (Understanding)
If $A = \begin{pmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{pmatrix}$, then $A^n$ equals to (Understanding)
- (a)$\begin{pmatrix} a^n & 0 & 0 \\ 0 & a^n & 0 \\ 0 & 0 & a^n \end{pmatrix}$
- (b)$\begin{pmatrix} a & 0 & 0 \\ 0 & a^n & 0 \\ 0 & 0 & a \end{pmatrix}$
- (c)$\begin{pmatrix} a^n & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a^n \end{pmatrix}$
- (d)$\begin{pmatrix} na & 0 & 0 \\ 0 & na & 0 \\ 0 & 0 & a^n \end{pmatrix}$
Answer
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From ISC 2026 Specimen Mathematics Paper 1, question 1(vi).