I'm self-studying quantum mechanics and have a question regarding the commutator.
Since the commutator of two operators is defined as
$[A,B]$ = $AB$ - $BA$
Assuming that these operators do not commute, does that mean that the value of, say $AB$ = (commutator) $+BA$
For example, the commutator between position $x$ and momentum $p$ is $[x,p] = xp-px$ = $i\hbar$
Does it follow that $xp = i\hbar + px$