Hello everyone!

I'm stuck on this particular concept...

$\displaystyle AB=AC \ \Rightarrow \ A(B-C)=0.$ Soooo when is it that $\displaystyle B-C=0$ i.e. $\displaystyle B=C \ ... \ (1)$ but probably if $\displaystyle A^{-1}$ exists then we can multiply to the right by $\displaystyle A^{-1}$ so we get $\displaystyle (1)$. But how can we know before hand?

Thanks!