Given:

In matrix A, there are 2 rows and 3 columns.

∴ A is a 2 × 3 matrix

In matrix B, there are 3 rows and 2 columns.

∴ B is a 3 × 2 matrix

So, the product matrix AB will be

∴ the order of AB is 2 × 2 matrix

and the order of product matrix BA will be

∴ the order of BA is 3 × 3 matrix.