Question

Find (AB)^-1 if

`A=[(1,2,3),(1,-2,-3)], B=[(1,-1),(1,2),(1,-2)]`

 

Answer 1

`A=[(1,2,3),(1,-2,-3)], B=[(1,-1),(1,2),(1,-2)]`

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

= `[[6,-3],[-4,1]]`

`(AB)^-1(AB)=I`

`(AB)^-1[[6,-3],[-4,1]]=[[1,0],[0,1]]`

`"Using "R_1 -> 1/6R_1`

`(AB)^-1[[1,-1/2],[-4,1]]=[[1/6,0],[0,1]]`

`"Using " R_2 ->R_2+4R_1`

`(AB)^-1[[1,-1/2],[0,-1]]=[[1/6,0],[2/3,1]]`

`"using "R_2->(-1)R_2`

`(AB)^-1[[1,-1/2],[0,1]]=[[1/6,0],[-2/3,-1]]`

`"Using " R_1->R_1+(1/2)R_2`

`(AB)^-1[[1,0],[0,1]]=[[-1/6,-1/2],[-2/3,-1]]`

`(AB)^-1I=[[-1/6,-1/2],[-2/3,-1]]`

`(AB)^-1=[[-1/6,-1/2],[-2/3,-1]]`