Question

If
a.b =
a.c then prove that a = 0 or b=c

Answer 1

Heya user,

If ab = ac, Assume : b ≠ c;
Then, ab = ac holds true only for b = c;

[ Hence, our assumption is wrong ] => b = c;

Again, for a = 0, b = c;
----------------------------------> ab = ac
===================> a = a;
====================> a / a = 1; [ which is not true '.' 0/0 -- NA ]

Hence, if ab = ac, either a = 0; or b = c;

_____________________________________________________________

Or else,
if ab = ac;
------> ab - ac = 0
-------> a ( b - c ) = 0
====> Either a = 0; or b = c, satisfies the eqn.

Hence, either a = 0, or b = c;