Find the value for c in the following n by n inverse if A n

Find the value for c in the following n by n inverse: if A = [n - 1. -1 -1 n. -1... -1 -1 -1 -1 n] then A^-1 = 1/n + 1 [c n. 1 1 c. 1... 1 1 1 1 c].]

Solution

This is the theorem identity, when we calculate the inverse of the matrix

A^(-1) = 1/|A| adj(A)

The given property enables that the value of Det(A) = n+1. hence the value will be the adjoint of A

which will be equal to (n+1)+(n+1) = 2n+2

Hence the value of c will be equal to 2, that will satisfy this equation