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Question
Answer the following question:
If A = `[(4, -1, -4),(3, 0, -4),(3, -1, -3)]`, show that A2 = I
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Solution
A2 = A·A
= `[(4, -1, -4),(3, 0, -4),(3, -1, -3)] [(4, -1, -4),(3, 0, -4),(3, -1, -3)]`
= `[(16 - 3 - 12, -4 + 0 + 4, -16 + 4 + 12),(12 + 0 - 12, -3 + 0 + 4, -12 + 0 + 12),(12 - 3 - 9, -3 - 0 + 3, -12 + 4 + 9)]`
= `[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
= I
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