The question is:

Let

A be a skew–symmetric n×n–matrix with entries in $\displaystyle R$, i.e. $\displaystyle A^T=-A$

Prove that In+A is an invertible matrix.

I have tried solving this both algebraically and non-algebraically. Algebraically I have started with the fact In+A=In-A, played around starting with there, including multiplying both sides by a nxn invertible matrix B, however never really get anywhere there.

Other then that, things that I have noticed that probably are of importance is the fact that the diagonals of the matrix In+A will be all ones, however im not sure if i need to use that and if so how how.

Any help would be greatly appreciated :)