Are AB and BA both defined if they are square matrices?

[georgeh]

So i have the following question
a) Show that if AB and BA are both defined, then AB and BA are square matrices..
this is what i tried doing..
If AB and BA are both tdefined then
A=[n x p ] matrix
B=[p x l ] matrix
AB=[nxl] matrix
IF and only IF l=n, then BA will be defined.
then BA=[p x p] matrix
and
AB=[l x l] matrix
then by definition both AB and BA will be square matrices..
is this correct? i think it is wrong.

 

[0rthodontist]

That's correct.