A, B, C are three non-null square matrices of the same order, wri… - Vidyadip

Question

A, B, C are three non-null square matrices of the same order, write the condition on A such that AB = AC ⇒ B = C.

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Answer

Consider AB = AC.

On multiplying both sides by A^-1, we get

AA^-1B = AA^-1

⇒ IB = IC [Because AA^-1 = I where I is the identity matrix]

⇒ B = C

Therefore, the required condition is A must be invertible or $|\text{A}|\neq0$.

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