Find the inverse of the following :
`[[x,-x],[x,x^2]]`,x ne 0, x ne -1`

Explanation

Let A=`[[x,-x],[x,x^2]]`,x ne 0, x ne -1`
`therefore absA=[[x,-x],[x,x^2]]=x^3+x^2=x^2(x+1) ne 0`
`therefore C_11=x^2, C_12=-x, C_21=x, C_22=x`
Let B=`[[C_11,C_12],[C_11,C_22]]=[[x^2,-x],[x,x]]`
`therefore adjA=B.=[[x^2,x],[-x,x]]`
`therefore A^-1 =(adjA)/(absA)= 1/(x^2(x+1)) [[x^2,x],[-x,x]]`
`[[1/(x+1),1/(x(x+1))],[(-1)/(x(x+1)),1/(x(x+1))]]`