This is probably a simple problem, but I just fell in love with that
Prove that for any , the square matrix consisting in only 1's in the diagonal and n everywhere else is always invertible.
The inverse is :
where and is the size of the matrix .
To obtain the determinant , not only the residue ...
Consider the system of the linear equations :
and note that is your matrix , let it be ( If i read the problem correctly )
Let be the quantity then we have
I believe it is true that