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  • Explain solution RD Sharma class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 9 maths

Explain solution RD Sharma class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 9 maths

Answers (1)

Answer:

A4 =  81I

 Hint:

Use the basic concept of matrix multiplication.

 Given:

A=\left[\begin{array}{lll} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{array}\right]

 Solution:

\begin{aligned} &A=\left[\begin{array}{lll} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{array}\right]=3\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]\\ &\text { Therefore, } A^{4}=(3 I)^{4}=81 I\\ &\text { Or }\\ &A^{4}=\left[\begin{array}{ccc} 81 & 0 & 0 \\ 0 & 81 & 0 \\ 0 & 0 & 81 \end{array}\right] \end{aligned}

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Gurleen Kaur

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