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Question
If f(x) = x2 − 2x − 3 then find f(A) when A = `[(1, 2),(2, 1)]`
Solution
f(A) = A2 − 2A − 3I
A2 = `[(1, 2),(2, 1)] [(1, 2),(2, 1)]`
= `[(1 +4, 2 + 2),(2 + 2, 4 + 1)]`
= `[(5, 4),(4, 5)]`
∴ f(A) = `[(5, 4),(4, 5)] - [(2, 4),(4, 2)] - [(3, 0),(0, 3)]`
= `[(5 - 2 - 3, 4 - 4 - 0),(4 - 4 - 0, 5 - 2 - 3)]`
= `[(0, 0),(0, 0)]`
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