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Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 9 Maths Textbook Solution.

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

Hint: Here we find that if we use the concept of matrix transpose, we can use also matrix algebra

Given: A_{T}=\begin{bmatrix} \cos x &\sin x \\ -\sin x & \cos x \end{bmatrix}


AA^{T}=\begin{bmatrix} \cos x &-\sin x \\ \sin x & \cos x \end{bmatrix}\begin{bmatrix} \cos x &\sin x \\ -\sin x & \cos x \end{bmatrix}

=\begin{bmatrix} \cos^{2} x+\sin^{2} x &\cos x\sin x-\sin x\cos x \\ \sin x \cos x-\cos x\sin x& \sin^{2}x\cos^{2} x \end{bmatrix}

= \begin{bmatrix} 1 &0 \\ 0 & 1 \end{bmatrix} because \left [ \cos^{2}x+\sin^{2}x=1 \right ]

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