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Question
If A = `[(1, 3), (3, 1)]`, Show that A2 - 2A is a scalar matrix.
Solution
A2 = A . A
= `[(1,3), (3, 1)] [(1,3), (3, 1)]`
= `[(10, 6), (6, 10)]`
A2 - 2A = `[(10, 6), (6, 10)] - 2[(1, 3), (3, 1)]`
A2 - 2A = `[(10, 6), (6, 10)] - [(2, 6), (6, 2)]`
A2 - 2A = `[(8, 0), (0, 8)]`
∴ A2 - 2A is a scalar matrix.
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