On invertibility of a special matrix - Hilbert matrix I want to know how to prove that the below matrix is invertible 
\begin{pmatrix} 1 & \frac { 1 }{ 2 }  & ... & \frac { 1 }{ n }  \\ \frac { 1 }{ 2 }  & \frac { 1 }{ 3 }  & ... & \frac { 1 }{ n+1 }  \\ ... & ... & ... & ... \\ \frac { 1 }{ n }  & \frac { 1 }{ n+1 }  & ... & \frac { 1 }{ 2n-1 }  \end{pmatrix}
and that the inverse matrix has integer entries.

Here is the the article on Wikipedia with this matrix.
