Question

State True or False:
If $A$, $B$ and $C$ are square matrices of same order, then $AB=AC$ always implies that $B=C$.

• A. False
• B. True

Answer 1

The correct option is A False

We have $AB=AC$
Let $A$ is invertible
Pre multiply by $A^{-1}$ on both sides
$A^{-1}AB=A^{-1}AC$
$\Rightarrow IB=IC$ $[\because A{A}^{-1}=I=A^{-1}A]$
$\Rightarrow B=C$
$\Rightarrow AB=AC$ always implies that $B=C$ if and only if $A$ is invertible.
Hence, the given statement is false.