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Question
Choose the correct answer from the given alternatives in the following question:
If A = `[("cos"alpha,-"sin"alpha),("sin"alpha,"cos"alpha)]`, then A-1 = _____
Options
`[(1/("cos"alpha),-1/("sin" alpha)),(1/("sin"alpha),1/("cos"alpha))]`
`[("cos"alpha,"sin"alpha),(-"sin"alpha, "cos"alpha)]`
`[(-"cos"alpha,"sin"alpha),(-"sin"alpha, "cos"alpha)]`
`[(-"cos"alpha,"sin"alpha),("sin"alpha, -"cos"alpha)]`
Solution
`[("cos"alpha,"sin"alpha),(-"sin"alpha, "cos"alpha)]`
Explanation:
A = `[("cos"alpha,-"sin"alpha),("sin"alpha,"cos"alpha)]`
|A| = cos2α + sin2α = 1
A−1 = `1/|"A"| "Adj"("A") = 1/1 [("cos"alpha,"sin"alpha),(-"sin"alpha, "cos"alpha)]`
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