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Question
If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A–1 = A′, find value of α
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Solution
Here, A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`
Given that: A–1 = A′
Pre-multiplying both sides by A
AA–1 = AA′
⇒ I = AA′ ......[∵ AA–1 = I]
⇒ `[(1, 0),(0, 1)] = [(cosalpha, sinalpha),(-sinalpha, cosalpha)] [(cosalpha, - sinalpha),(sinalpha, cosalpha)]`
⇒ `[(1, 0),(0, 1)] = [(cos^2alpha + sin^2alpha, -sinalpha cosalpha + sinalpha cosalpha),(-sinalpha cosalpha + cosalpha sinalpha, sin^2alpha + cos^2alpha)]`
⇒ `[(1, 0),(0, 1)] = [(1, 0),(0, 1)]`
Hence, it is true for all values of a.
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