Question

If A = `[(1, -2),(3, 0)], B = [(0, -2),(2, 1)]` is AB = BA? Also, conclude your result.

Answer 1

A = `[(1, -2),(3, 0)]`

B = `[(0, -2),(2, 1)]`

AB = `[(1, -2),(3, 0)] [(0, -2),(2, 1)]`

= `[(1 xx 0 + (-2) xx 2, 1 xx (-2) + (-2) xx 1),(3 xx 0 + 0 xx 2, 3 xx (-2) + 0 xx 1)]`

= `[(-4, -4),(0, -6)]`

BA = `[(0 xx 1 + (-2) xx 3, 0 xx (-2) + (-2) xx 0),(2 xx 1 + 1 xx 3, 2 xx (-2) + 1 xx 0)]`

= `[(-6, 0),(5, -4)]`

AB ≠ BA

∴ This result demonstrates that matrix multiplication is not commutative, which means that the order in which two matrices are multiplied matters.