If `A=[[3,1],[7,5]]`, verify that
`A. ("adj " A) ``= ("adj " A). A= |A|. I.`

Explanation

We have
`A=[[3,1],[7,5]]=(15-7)=8!=0`.
The cofactors of the elements of `|A|` are given by
`A_(11)=5,A_(12)=-7,`
`A_(21)=-1,A_(22)=3`.
`:." " (adj A)=[[5,-7],[-1,3]]'=[[5,-1],[-7,3]]`.
`:." "A. (adj A)=[[3,1],[7,5]] [[5,-1],[-7,3]]`
`=[[15-7" "-3+3],[35-35" "-7+15]]=[[8,0],[0,8]]`
`=8.[[1,0],[0,1]]=8I=|A|.I" "[:' |A|=8]`
`And, (adj A). A=[[5,-1],[-7,3]][[3,1],[7,5]]`
`[[15-7" "5,-5],[-21+21,-7+15]]=[[8,0],[0,8]]`
`=8.[[1,0],[0,1]]=8I = |A|.I" "[:' |A|=8]`.
Hence, `A .(adj A)=(adj A). A=|A|.I`.