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Question
If A, B and C are square matrices of same order, then AB = AC always implies that B = C
Options
True
False
Solution
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.
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