Finding the inverse of a matrix using gaussian elimination

Question

It's given the matrix A such that:

 [ 0  1  1 ... 1  1]
 |-1  0  1 ... 1  1|
 |-1 -1  0 ... 1  1|
 |    .         .  |
 |    .         .  |
 |    .         .  |
 |-1 -1 -1 ... 0  1|
 [-1 -1 -1 ...-1  0]

Can someone help me find the inverse of this matrix using Gaussian elimination I tried adding the last row to all other rows but it doesn't work. Can someone tell me just some few steps.Any help would be appreciated.Thank you!

Answer 1

HINT

I am not certain that this will help you, but notice that for even matrix dimensions (i.e. your $n\times n$ matrix has $n=2k$, $k \in \mathbb{N}$) the determinant is equal to $0$ and thus the matrix is not invertible.

Also, if $n=2k+1$, $k \in \mathbb{N}$, then the determinant is equal to $1$.

So you need to focus on the odd case..