The question is:
Let
A be a skew–symmetric n×n–matrix with entries in , i.e.
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