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Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 42 Maths Textbook Solution.

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Hint: Here we use basic concept of identity matrix


A=\begin{bmatrix} \cos \alpha & -\sin \alpha\\ \sin \alpha & \cos \alpha \end{bmatrix} is idetnify matrix

Find \alpha

Solution: A_{2\times2}=\begin{bmatrix} \cos \alpha &-\sin \alpha \\ \sin \alpha & \cos \alpha \end{bmatrix}_{2\times2}

A is identity matrix A=

\begin{aligned} &A \text { is identity matrix } A=[\cos \cos \alpha-\sin \sin \alpha \sin \sin \alpha \cos \cos \alpha]_{2 \times 2}\\ &=\left[\begin{array}{lll} 1001 \end{array}\right]_{2 \times 2} \cos \cos \alpha=1 \sin \sin \alpha=0 \alpha=0^{\circ}\left[\text { For } \alpha \in 0^{\circ} \text { to } 360^{\circ}\right] \alpha\\ &=0 \text { radian } \end{aligned}

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