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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 14 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 14 Maths Textbook Solution.

Answers (1)

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Answer: A^{3}=A=\begin{bmatrix} -1 & 0 &0 \\ 0& -1 & 0\\ 0 & 0&-1 \end{bmatrix}

Hint: Here, we use the concept of matrix multiplication

Given: A=\begin{bmatrix} -1 & 0 &0 \\ 0& -1 & 0\\ 0 & 0&-1 \end{bmatrix}A^{3}=?

Solution:

A^{3}=\left [-1\: 0 \: 0 \: 0 \: -1\: 0\: 0 \: 0 \: -1 \right ] \times A^{2}A^{2}=\left [ -1 \:0\: 0\: 0 \:-1\: 0\: 0\: 0\: -1 \right ] \times\left [-1\: 0\: 0\: 0\: -1\: 0 \:0 \:0\: -1 \right ] =\left [ 1 \:0\: 0\: 0\: 1 \:0 \:0 \:0 \:1 \right ] A^{3}=\left [ 1\: 0\: 0\: 0\: 1\: 0\: 0\: 0\: 1 \right ] \times\left [ -1 \:0 \:0 \:0 \:-1\: 0\: 0\: 0\: -1 \right ]

A^{3}=\begin{bmatrix} -1+0+0 &0+0+0 &0+0+0 \\ 0+0+0 &0+0-1 &0+0+0 \\ 0+0+0 &0+0+0 &0+0-1 \end{bmatrix}

A^{3}=\begin{bmatrix} -1 & 0 &0 \\ 0& -1 & 0\\ 0 & 0&-1 \end{bmatrix}

A^{3}=A

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