Find adjoint of the matrice in`[(1, 2),( 3, 4)]`

Explanation

Let `[(1, 2),( 3, 4)]`

Calculating `adj A`

`adj A=[[A_(11),A_(21)],[A_(12),A_(22)]]`

Minor of `a_(11)=M_(11)=4, " " " " `Minor of `a_(12)=M_(12)=3`

Minor of `a_(21)=M_(21)=2, " " " " `Minor of `a_(22)=M_(22)=1`


Now, Co factor of `a_(ij)=A_(ij)=(-1)^(i+j)M_(ij)`

Co factor of `a_(11)=A_(11)=(-1)^(1+1)M_(11)=(-1)^2(4)=4, `
Co factor of `a_(12)=A_(12)=(-1)^(1+2)M_(12)=(-1)^3(3)=-3`

Co factor of `a_(21)=A_(21)=(-1)^(2+1)M_(21)=(-1)^3(2)=-2, `
Co factor of `a_(22)=A_(22)=(-1)^(2+2)M_(22)=(-1)^4(1)=1`


`therefore` `adj A=[[4,-2],[-3,1]]`