Question

If  A = `[(4, 3, 2),(-1, 2, 0)],"B" = [(1, 2),(-1, 0),(1, -2)]` show that matrix AB is non singular.

Answer 1

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

= `[(4 - 3 + 2, 8 + 0 - 4),(-1 - 2 + 0, -2 + 0 + 0)]`

= `[(3, 4),(-3, -2)]`

∴ |AB| = `|(3, 4),(-3 ,-2)|`

= – 6 + 12
= 6 ≠ 0
∴ AB is a non-singular matrix.