Question

Is it possible to define the matrix AB and BA when :
A has 4 rows and B has 4 columns

Answer 1

AB = $A_{4\times p}{B}_{q\times 4}$ and $BA=B_{q\times 4}{A}_{4\times p}$
For AB. It depends on the number of columns of A and number of rows of B i.e., p,q and both should be equal .
For BA, It is always defined because the number of columns in prefactor B is the same as the number of rows in post - factor A i.e., 4 = 4.