Question

Is it possible to define the matrix AB and BA when :
(a) A has 3 rows and B has 2 rows

Answer 1

Let AB = $A_{3\times p}{B}_{2\times q}$
The product AB is defined only when the number of columns in prefactor A i.e., p is the sam as the number of rows in post factor B i.e., 2,Since B has 2 rows therefore A should have 2 columns for AB to be defined i.e., p = 0
Also for BA to be defined the number of columns in prefactor B i.e., q should be same as number of rows in post - factor A i.e., 3 and hence B should have 3 columns .