Q2 of 307 Page 6

If and . Write the order of AB and BA.

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.

Express the matrix as the sum of a symmetric and skew-symmetric matrix and verify your result.

If A is an m × n matrix and B is n × p matrix does AB exist? If yes, write its order.

If and , write AB.

If , write AA^T.