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.

Question

Find AB,

If A = \(\begin{bmatrix} 1 & 2 & 3 \\[0.3em]1 & -2 &-3 \\[0.3em] \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & -1 \\[0.3em]1 & 2 \\[0.3em] 1& -2\end{bmatrix}\) 

Examine whether AB has inverse or not.

[1,2,3,1,-2,-3] 

[1,-1,1,2,1,-2]

Answer 1

Given,

A = [1,2,3,1,-2,-3] and 

B = [1,-1,1,2,1,-2]

∴ A is a non-singular matrix.

Hence,

(AB)^-1 exist.