Question

If A = `[(2, 3, -1),(1, 4, 2)]` and B = `[(2, 3),(4, 5),(2, 1)]`, then AB and BA are defined and equal.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

A = `[(2, 3, -1),(1, 4, 2)]` and B = `[(2, 3),(4, 5),(2, 1)]`

Since AB is defined

∴ AB = `[(2, 3, -1),(1, 4, 2)] [(2, 3),(4, 5),(2, 1)]`

= `[(4 + 12 - 2, 6 + 15 - 1),(2 + 16 + 4, 3 + 20 + 2)]`

= `[(14, 20),(22, 25)]`

BA is also defined.

∴ BA = `[(2, 3),(4, 5),(2, 1)] [(2, 3, -1),(1, 4, 2)]`

= `[(4 + 3, 6 + 12, -2 + 6),(8 + 5, 12 + 20, -4 + 10),(4 + 1, 6 + 4, -2 + 2)]`

= `[(7, 18, 4),(13, 32, 6),(5, 10, 0)]`

So AB ≠ BA.