If A is a matrix of order (m × n) such that AB and BA are both defined, then B is a/an :

1. m × n matrix

2. n × m matrix

3. m × m matrix

4. n × n matrix

If A is of order m × n:

For matrix multiplication AB to exist, the number of columns of A must equal the number of rows of B.

Number of rows in B = n

For matrix multiplication BA to exist, the number of columns of B must be equal to the number of rows of A.

Number of columns in B = m.

B is of order = n × m.

Hence, option 2 is the correct option.