Question

Find AB, if A = `((1,2,3),(1,-2,-3))` and B = `((1,-1),(1,2),(1,-2))`. Examine whether AB has inverse or not.

Answer 1

AB = `((1,2,3),(1,-2,-3)) xx ((1,-1),(1,2),(1,-2))`

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

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

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

∴ |AB| = `|(6,-3),(-4,1)| = 6 - 12 = - 6 ≠ 0`

∴ AB is a non-singular matrix.

Hence, (AB)^-1 exists.