If A = $[\begin{matrix} cosα & - sinα \\ sinα & cosα \end{matrix}]$ , then for what value of α is A an identity matrix?

Solution

Matrix A is a matrix of order 2.

Identity matrix of second order is $[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

For A to be an identity matrix,

$[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] = [\begin{matrix} cosα & - sinα \\ sinα & cosα \end{matrix}] \Rightarrow cosα = 1 and sinα = 0 \Rightarrow cosα = \cos 0 ° and sinα = \sin 0 ° \Rightarrow α = 0 ° Thus, for α = 0 °, A is an identity matrix .$

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If A = $[\begin{matrix} cosα & - sinα \\ sinα & cosα \end{matrix}]$ , then for what value of α is A an identity matrix?

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Matrices

If A = cosα - sinαsinα cosα , then for what value of α is A an identity matrix?

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Mock Test Series

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If A = $[\begin{matrix} cosα & - sinα \\ sinα & cosα \end{matrix}]$ , then for what value of α is A an identity matrix?