Division

When discussing inverse matrices (and more generally inverses in
general non-commutative groups or rings),
one should explain why you -cannot- naively write division or
fractions:
$\frac{A}{B}$ -doesn't make sense-,
because it doesn't specify which side to divide on.

Indeed, there is a very good notation that exactly specifies it,
namely:
$A/B = AB^{-1}$
$B\backslash A = B^{-1}A$
[and indeed we do use the / (slash/slant) operation
 in some axiomatizations of groups,
 and in (co)homology]

The great value here is that by -naming- the possible ways of -giving
meaning- to an idea, we help show that there -is- a difference.
[And conversely, beware of giving separate names to the same thing:
 this suggests that they are different things.]

Naming is -very- useful, b/c it gives you a -mental hook-.
