Question

If `A=[[2,-2],[4,3]]` then find `A^-1` by adjoint method.

Answer 1

Given :`A==[[2,-2],[4,3]]`

`|A|=|[2,-2],[4,3]|=6+8=14ne0`

`therefore A^-1 " exist"`

`M_11=3           A_11=(-1)^2 3=3`

`M_12=4           A_11=(-1)^3 3=-4`

`M_21=-2          A_11=(-1)^3 (-2)=2`

`M_22=2           A_11=(-1)^2 3=2`

 

`Adj. (A)=[[A_11,A_12],[A_21,A_22]]=[[3,-4],[2,2]]`

`=[[3,2],[-4,2]]`

`therefore A^-1=(Adj(A))/|A|`

`=1/14[[3,2],[-4,2]]`