Help!! System of equations!

[RobandJoanna]

For a natural number define the n*n matrix A = (aij) by setting aij = min(i,j). Write down the matrix a for a few values of n = 2,3,4...... Show that A is invertible and find its inverse.
Hence or otherwise show that the system of equations Ax =b , where x=(x1,....xn) and b=(b1.....bn) has a unique solution.

Anyone help with how to solve that?
Thanks
Rob and Joanna!

[shmoe]

Have you tried n=2, 3, and 4 at least?

Write them down and try to reduce to the identity by row operations. Should be easy. You shold be able to find inverse in each case too.