Is it possible to determine with little or no calculation the rank of a $5 \times 5$ or any square matrix if it has an inverse matrix?

I found the requirements for an inverse:

> 
> * The matrix must be square (same number of rows and columns).
> * The determinant of the matrix must not be zero. This is instead of the real number not being zero to have an inverse, the determinant must not be zero to have an inverse.
> 
> 
> 

I don't see any word on the rank here. 

Any help is appreciated.