Question

If A = `[(2, 5),(1, 3)] "B" = [(1, -1),(-3, 2)]` , find AB and BA, Is AB = BA ?

Answer 1

A = `[(2, 5),(1, 3)]`

B = `[(1, -1),(-3, 2)]`

∴ A x B = `[(2, 5),(1, 3)] xx [(1, -1),(-3, 2)]`

= `[(2 - 15, -2 + 10),(1 - 9, -1 + 6)]`

= `[(-13, 8),(-8, 5)]`
and
B x A = `[(1, -1),(-3, 2)] xx [(2, 5),(1, 3)]`

= `[(2 - 1, 5 - 3),(-6 + 2, -15 + 6)]`

= `[(1, 2),(-4, -9)]`
Hence AB ≠ BA.