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Question
If A = `[(costheta, sintheta),(-sintheta, costheta)]` prove that AAT = I
Solution
AT = `[(costheta, - sintheta),(-sintheta, costheta)]`
A · AT = `[(costheta, sintheta),(- sintheta, costheta)] [(costheta, - sintheta),(sintheta, costheta)]`
= `[(cos^2theta + sin^2theta, -costhetasintheta + costhetasintheta),(-sintheta costheta + costheta sintheta, sin^2theta + cos^2theta)]`
= `[(1, 0),(0, 1)]`
= I
Hence it is proved.
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