Question

Give an example of matrices A, B and C such that AB = AC, where A is nonzero matrix, but B ≠ C.

Answer 1

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