Proving inverse of two matrices Given the identity matrix $I_n$ and a matrix $J_n$ with only 1's as every element.
I must prove that if $n>0$ then $(I_n - J_n)^{-1} = I_n - \frac{1}{n-1} J_n$
I'm trying to understand if there is some sort of theorem that states that $(I_n - J_n)^{-1} = I_n^{-1} - J_n^{-1}$ or something like that?

Just multiply out the things that are supposed to be inverses of each other, and check that it gives $I_n$.
