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Question
Show by an example that for A ≠ O, B ≠ O, AB = O
Solution
Let A = `[(1, -1),(-1, 1)]` and B = `[(1, 1),(1, 1)]`
AB = `[(1, -1),(-1, 1)][(1, 1),(1, 1)]`
⇒ AB = `[(1 - 1, 1 - 1),(-1 + 1, -1 + 1)]`
= `[(0, 0),(0, 0)]` = O
Hence, A = `[(1, -1),(-1, 1)]` and B = `[(1, 1),(1, 1)]`
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