# Consider the matrix A = [[c,1,0],[1,c,1],[0,1,c]] For the values of c in (a), find the inverse of A.

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### 1 Answer

Given matrix is `A=[[c,1,0],[1,c,1],[0,1,c]]` .

Inverse of the matrix A will exist only when `det A!=0` .

Now det A=`c^3-2c!=0` .

i.e. `c!=0` and `c!=+-sqrt2` .

Now for all real values of `c!=0,+-sqrt2` we calculate the inverse of the given matrix A as under-

The minors for the matrix A are `a_11=c^2-1, a_12=-c, a_13=1,a_21=-c, a_22=c^2, a_23=-c, a_31=1,a_32=-c, a_33=c^2-1`

`Adj A=[[c^2-1,-c,1],[-c,c^2,-c],[1,-c,c^2-1]]`

` A^-1=(Adj A)/det A.`

`A^-1={1/(c^3-2c)}[[c^2-1,-c,1],[-c,c^2,-c],[1,-c,c^2-1]]`

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