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 $AA^{-1}B = AA^{-1}$
$\Rightarrow IB = IC$ [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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