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Question
If A = `[(cos α, sin α), (-sin α, cos α)]`, then verify that A' A = I
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Solution
Given, A = `[(cos α, sin α), (-sin α, cos α)]`
So, A' = `[(cos α, -sin α), (sin α, cos α)]`
Now, A' A = `[(cos α, -sin α), (sin α, cos α)] xx [(cos α, sin α), (-sin α, cos α)]`
= `[(cos^2 α + sin^2 α, cos α sin α - sin α cos α),(sin α cos α - cos α sin α, sin^2 + cos^2 α)]`
= `[(1, 0),(0, 1)]` = I ...[∵ sin2 α + cos2 α = 1]
Hence, A' A = I
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