Question

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Answer 1

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01. Two matrixes A and B are given. Express B^-1 through x and A.

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Answer 2

༒ Given ➽

$A = \begin{bmatrix}cos \theta& - sin \theta \\ sin \theta&cos \theta \end{bmatrix}$

And

$B = \begin{bmatrix}cos \theta& sin \theta \\ - sin \theta&cos \theta \end{bmatrix}$

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༒ To Prove ➽

$\large AB = I$

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༒ Proof ➽

LHS:-

$AB = \begin{bmatrix}cos \theta& - sin \theta \\ sin \theta&cos \theta \end{bmatrix}\begin{bmatrix}cos \theta& sin \theta \\ - sin \theta&cos \theta \end{bmatrix} \\ \\ = \begin{bmatrix}cos {}^{2} \theta + {sin}^{2} \theta & cos \theta sin \theta - sin \theta cos \theta \\ sin \theta cos \theta - cos \theta sin \theta& {sin}^{2} \theta + cos {}^{2} \theta \end{bmatrix} \\ \\ = \begin{bmatrix}1& 0 \\ 0&1\end{bmatrix} = I$

= RHS

Hence Proved

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