Find the value of x for which the matrix [[6,x],[7,-6]] is its own inverse.

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`A=[[6,x],[7,-6]]` ,by given condition we need to determine x such that

`A.A=[[1,0],[0,1]]`

Substitute value of A

`[[6,x],[7,-6]][[6,x],[7,-6]]=[[1,0],[0,1]]`

`[[36+7x,0],[0,7x+36]]=[[1,0],[0,1]]`

`36+7x=1`

`7x=-35`

`x=-5`

Ans.

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