Question

If A = `[(0, 2),(5, -2)]`, B = `[(1, -1),(3, 2)]` and I is a unit matrix of order 2 × 2, find B²A

Answer 1

B² = `[(1, -1),(3, 2)][(1, -1), (3, 2)]`

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

= `[(1- 3, -1-2),(3 + 6, -3 + 4)]`

= `[(-2 ,-3),(9, 1)]`

B²A = `[(-2, -3),(9, 1)][(0, 2),(5, -2)]`

= `[(-2 xx 0 + (-3) xx 5, (-2) xx 2 + (-3) xx (-2)),(9 xx 0 + 1 xx 5, 9 xx 2 + 1 xx (-2))]`

= `[(0 - 15, -4 + 6),(0+ 5, 18 - 2)]`

= `[(-15, 2),(5, 16)]`