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Question
If A = `[(4, 2),(1,1)]`, find (A – 2I)(A – 3I).
Solution
A – 2I = `[(4, 2),(1, 1)] - 2[(1, 0),(0, 1)]`
= `[(4, 2),(1,1)] - [(2, 0),(0, 2)]`
= `[(2, 2),(1, -1)]`
A – 3I = `[(4, 2),(1,1)] - 3[(1, 0),(0, 1)]`
= `[(4, 2),(1, 1)] - [(3, 0),(0, 3)]`
= `[(1, 2),(1, -2)]`
(A – 2I)(A – 3I) = `[(2, 2),(1, -1)][(1, 2),(1, -2)]`
= `[(2 + 2, 4 - 4),(1 - 1, 2 + 2)]`
= `[(4, 0),(0, 4)]`
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