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  • Please Solve R .D.Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions Question 8 Maths Textbook solution.

Please Solve R .D.Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions Question 8 Maths Textbook solution.

Answers (1)

Answer: The correct option is (C).

Given:\left[\begin{array}{ccc} a^{n} & 0 & 0 \\ 0 & a^{n} & 0 \\ 0 & 0 & a^{n} \end{array}\right]

Solution:

\begin{aligned} &\text { Let } A=\left[\begin{array}{lll} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{array}\right] \\ &\Rightarrow A^{n}=\left[\begin{array}{lll} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{array}\right] \times\left[\begin{array}{lll} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{array}\right] \ldots \text { n times } \\ &\Rightarrow A^{n}=\left[\begin{array}{ccc} a^{n} & 0 & 0 \\ 0 & a^{n} & 0 \\ 0 & 0 & a^{n} \end{array}\right] \end{aligned}

So, the correct option is option (C).

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