Class 12

Math

Algebra

Matrices

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

- $3×4$
- $3×3$
- $4×4$
- $4×3$

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.