Let A; B; C be square matrices of the same order n. If A is a non singular matrix; then `AB = AC` then `B = C`

Explanation

If AB=AC=0 then it can be possible that B and C are two non-zero matrices such that
`BneC`
`therefore A.B=0=A.C`
Let `A=[{:(1,0),(0,0):} ]B=[{:(0,0),(1,3):}]`
and `C=[{:(0,0),(3,1):}]`
`therefore AB=[{:(1,0),(0,0):}][{:(0,0),(1,3):}]=[{:(0,0),(0,0):}]`
and `AC=[{:(1,0),(0, 0):}][{:(0,0),(1,3):}]=[{:(0,0),(0,0):}]`
and `AC=[{:(1,0),(0,0):}][{:(0,0),(3,1):}]=[{:(0,0),(0,0):}]`
`rArr AB=AC` but `BneC`