proof of matrix singularity If anyone can help me with the next question I would appreciate it a lot.
Let $A$ and $B$ be $n*n$ matrices and let $C=A-B$. Show that if $Ax_0=Bx_0$ and  $x_0$ is not zero, then $C$ must be singular.
The first thing I don't get is the notation, what do $Ax_0$ and $Bx_0$ mean?
Thanks in advance :)

if $x_0 \neq 0$
$$Ax_0 = B x_0$$
then we have 
$$(A-B) x_0=0$$
that is we have $x_0 \neq 0$ such that $Cx_0=0$ which means $C$ is singular.
