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If \(\begin{bmatrix}cos\,\alpha & -sin\,\alpha \\[0.3em]sin\,\alpha & cos\,\alpha \\[0.3em]\end{bmatrix}\), then for what value of α, A is an identity matrix? |
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Answer» If A is identity matrix, Then, A = I2 \(\begin{bmatrix} cos\,\alpha & -sin\,\alpha \\[0.3em] sin\,\alpha & cos\,\alpha \\[0.3em] \end{bmatrix} \)= \(\begin{bmatrix} 1 & 0 \\[0.3em] 0 & 1 \\[0.3em] \end{bmatrix} \) On equating, we get ⇒ cos α = 1,sin α = 0 ⇒ α = 0 |
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