1.

If `A=[(2,-3),(3,5)]` then find `A^(-1)` by adjoint method.

Answer» Given, `A=[(2,-3),(3,5)]`
`|A|=2xx5-(-3)(3)=10+9=19!=0`
`:.A^(-1)` exists.
To find adjoint of A :
`M_(11)=5, A_(11)=(-1)^(2)*5=5`
`M_(12)=3, A_(12)=(-1)^(3)*3=-3`
`M_(21)=-3, A_(21)=(-1)^(3)*(-3)=3`
`M_(22)=2, A_(22)=(-1)^(4)*(2)=2`
`:.` Matrix of cofactors is `[(5,-3),(3,2)]`
`:.` Adj. `A=[(5,3),(-3,2)]`
We have,
`A^(-1)=(1)/(|A|)*`Adj.
`A=(1)/(19)[(5,3)/(-3,2)]`


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