If A is 3 × 4 matrix and B is a matrix such that A^TB and BA^T are both defined. Then, B is of the type

Order of A = 3 × 4

Order of A’ = 4 × 3

As A^TB and BA^T are both defined, so the number of columns in B should be equal to the number of rows in A’ for BA’ and also the number of columns in A’ should be equal to the number of rows in A’ for BA’.

So the order of matrix B = 3 × 4.

Option (A) is the answer.