Find `(AB)^(-1) " if "A = {:((1,2,3),(1,-2,-3)):}, B = {:((1,-1),(1,2),(1,-2)):}`

Find `(AB)^(-1) " if "A = {:((1,2,3),(1,-2,-3)):}, B = {:((1,-1),(1,2)

1.	Find `(AB)^(-1) " if "A = {:((1,2,3),(1,-2,-3)):}, B = {:((1,-1),(1,2),(1,-2)):}`
Answer» We have, `H=[{:(1,2,3),(1,-2,-3):}]and B=[{:(1,-1),(1,2),(1,-2):}]` Now `AB=[{:(1,2,3),(1,-2,-3):}][{:(1,-1),(1,2),(1,-2):}]` `AB=[{:(1+2+3,-1+4-6),(1-2-3,-1-4+6):}]` `AB=[{:(6-3),(-41):}` Now, we get `M_(11)=1,` `A_(11)=(-1)^(1+1)(1)=1` `M_(12)=-4,` `A_(12)=(-1)^(1+2)(-4)=4` `M_(21)=(-1)^(1+2)(-3)=3` `M_(22)=6,` `A_(22)=(-1)^(2+2)(6)=6` therefeforeadj.`(AB)=[{:(1,4),(3,6):}]^(T)=[{:(1,3),(4,6):}]` and `\|AB\|=\|{:(1,3),(4,6):}\|=6-12=-6ne0` `therefore` Using `A^(-1)=(1)/(\|A\|)adj. A` `therefore(AB)^(-1)=-1/6[{:(1,3),(4,6):}]` which is the required inverse.