Question

If A, B and C are square matrices of same order, then AB = AC always implies that B = C

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Let A = `[(1, 0),(0, 0)]`

B = `[(0, 0),(2, 0)]`

And C = `[(0, 0),(3, 4)]`

∴ AB = `[(1, 0),(0, 0)] [(0, 0),(2, 0)] = [(0, 0),(0, 0)]`

AC = `[(1, 0),(0, 0)] [(0, 0),(3, 4)] = [(0, 0),(0, 0)]`

Here AB = AC = 0 but B ≠ C.