SOLUTION: Suppose A is a 5 x 3 matrix, B is an r x s matrix and C is a 4 x 5 matrix. If At BC is defined, then what is the size of b

Since A is 5 x 3 matrix, the matrix  is 3 x 5 matrix (3 rows and 5 columns).


Since the matrix product   is defined, it implies that matrix B has 5 rows.


Since the matrix C is 4 x 5 matrix and the matrix product BC is defined, it implies that matrix B has 4 columns.


ANSWER.  Matrix B has 5 rows and 4 columns, i.e. is 5 x 4 matrix.