Isn't it always true?

Algebra Level 3

If provided that the matrix equation $AB=AC$ implies $B=C$ , then which statement is always correct for the square matrix $A$ ?

A

is symmetric matrix

A

is any matrix

A

is non-singular matrix

A

is singular matrix

2 solutions

Rishabh Jain
Jan 1, 2016

AB=AC

$\Rightarrow$ A^(-1)AB=A^(-1)AC

$\Rightarrow IB=IC$

$\Rightarrow B=C$

This is true only for a non singular matrix.

Aman Sharma
Nov 8, 2017

AB=AC => A(B-C)=O --(1) Since, B-C=O, therefore equation (1) have only trivial solution which is possible only if A is non singular