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