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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 15 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 15 Maths Textbook Solution.

Answers (1)

Answer: A^{4}=\begin{bmatrix} 81 & 0\\ 0 & 81 \end{bmatrix}

Hint: Here, we use the basic concept of matrix multiplication

Given: A=\begin{bmatrix}-3 & 0\\ 0 & -3 \end{bmatrix} find A^{4}

Solution:

A^{4}=A^{2}\times A^{2}

A^{2}= \begin{bmatrix} -3 & 0\\ 0 & -3 \end{bmatrix}\times\begin{bmatrix} -3 & 0\\ 0 & -3 \end{bmatrix}

A^{2}= \begin{bmatrix} 9+0 & 0+0\\ 0+0 & 0+9 \end{bmatrix}=\begin{bmatrix} 9& 0\\ 0 & 9 \end{bmatrix}

A^{2}\times A^{2}= \begin{bmatrix} 9 & 0\\ 0& 9 \end{bmatrix}\times\begin{bmatrix} 9& 0\\ 0 & 9 \end{bmatrix}

A^{4}= \begin{bmatrix} 81+0 & 0+0\\ 0+0& 81+0 \end{bmatrix}=\begin{bmatrix} 81& 0\\ 0 & 81 \end{bmatrix}

Note: Whenever you solve the matrix multiplication’s question must follow their rules.

 

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