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Question
Give an example of matrices A, B and C such that AB = AC, where A is nonzero matrix, but B ≠ C.
Solution
Let A = `[(1, 0),(0, 0)]`, B = `[(1, 1),(1, 0)]` and C = `[(1, 1),(1, 2)]` ......[∵ B ≠ C]
∴ AB = `[(1, 0),(0, 0)] [(1, 1),(1, 0)] = [(1, 1),(0, 0)]` ......(i)
And AC = `[(1, 0),(0, 0)] [(1, 1),(1, 2)] = [(1, 1),(0, 0)]` ......(ii)
From (i) and (ii)
We have AB = AC but B ≠ C
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