Question

If A is 3 × 4 matrix and B is a matrix such that A'B and BA' are both defined. Then, B is of the type
(a) 3 × 4
(b) 3 × 3
(c) 4 × 4
(d) 4 × 3

Answer 1

(a) 3 × 4

The order of A is 3 $\times$ 4. So, the order of A' is 4 $\times$ 3.

Now, both $A\text{'}B\mathrm{and}BA\text{'}$ are defined. So, the number of columns in A' should be equal to the number of rows in B for A'B.
Also, the number of columns in B should be equal to number of rows in A' for BA'.

Hence, the order of matrix B is 3 $\times$ 4.