'A' and 'B' are two matrices such that the order of 'A' is 3x4. If AB and BA are both defined, then order of B is

Analysis of the Problem:

We are given two matrices, 'A' and 'B', where the order of matrix 'A' is 3 × 4 (3 rows and 4 columns). We are tasked with determining the order of matrix 'B' such that both the matrix products AB and BA are defined. To solve this, we need to recall the rules of matrix multiplication:

• For the product AB to be defined, the number of columns in A must equal the number of rows in B.
• For the product BA to be defined, the number of columns in B must equal the number of rows in A.

Step-by-Step Solution:

1. Matrix A has dimensions 3 × 4:

This means matrix A has 3 rows and 4 columns.

2. For AB to be defined:

The number of columns in A (which is 4) must equal the number of rows in B. Therefore, the number of rows in B is 4.

3. For BA to be defined:

The number of columns in B must equal the number of rows in A (which is 3). Therefore, the number of columns in B is 3.

4. Order of matrix B:

From the above two conditions, the dimensions of matrix B must be 4 × 3 (4 rows and 3 columns).

Correct Option:

The correct order of matrix B is 4 × 3, which corresponds to Option 4.