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  4. The multiplicative inverse of A = [cos θ&-sin θ sin θ &cos θ ] is

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Q. The multiplicative inverse of $ A = \begin{bmatrix}cos\,\theta&-sin\,\theta \\ sin\,\theta &cos\,\theta \end{bmatrix} $ is

MHT CETMHT CET 2011

Solution:

$|A|=\cos ^{2} \theta+\sin ^{2} \theta=1$
adj (A) =$\begin{bmatrix}cos\theta&sin\theta\\ -sin\theta&cos\theta\end{bmatrix}$
$A^{-1} = \frac{adj(A)}{|A|}=\begin{bmatrix}cos\theta&sin\theta\\ -sin\theta&cos\theta\end{bmatrix}$