Question

If A is $3\times 4$ matrix and B is matrix such that A'B and BA' are both defined, then B is of the type.

• A. $3\times 4$
• B. $3\times 3$
• C. $4\times 4$
• D. $4\times 3$

Answer 1

The correct option is A $3\times 4$

Given that matrix A is 3 x 4.

Let the B matrix be P x Q.

Therefore, A' is 4 x 3.

Since A'B is defined, so number of columns of A' must be equal to number of rows of B, therefore, P = 3.

Also, BA' is defined, so the number of columns of B must be equal to number of rows of A', then Q = 4.

Therefore, matrix B is 3 x 4.