Question

If A + I = `[(1, 2, 0),(5, 4, 2),(0, 7, -3)]`, find the product (A + I)(A − I).

Answer 1

A + I = `[(1, 2, 0),(5, 4, 2),(0, 7, -3)]`    ...(1)

A = `[(1, 2, 0),(5, 4, 2),(0, 7, -3)]-"I"`

= `[(1, 2, 0),(5, 4, 2),(0, 7, -3)]-[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`

= `[(0, 2, 0),(5, 3, 2),(0, 7, -4)]`

(A + I)(A − I) = `[(1, 2, 0),(5, 4, 2),(0, 7, -3)]xx[(0, 2, 0),(5, 3, 2),(0, 7, -4)]-[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`

= `[(1, 2, 0),(5, 4, 2),(0, 7, -3)][(1, 2, 0),(5, 2, 2),(0, 7, -5)]`

= `[(-1 + 10 + 0, 2 + 4 + 0, 0 + 4 + 0),(-5 + 20 + 0 , 10 + 8 + 14, 0 + 8 - 10),(0 + 35 + 0, 0 + 14 - 21, 0 + 14 + 15)]`

 `[(9, 6, 4),(15, 32, -2),(35,-7,29)]`