I know this question has been asked and answered here: Can a matrix have a null space that is equal to its column space?. However, I'm not clear on the mechanism used to find an actual matrix so I figured I would make a new question. If this is inappropriate please flag or delete.
What I have done is let $A$ be a 4 x 4 matrix where $Null(A)=Col(A)$ (null space of A=Col Space of A). Therefore, the span of the columns of A = the null space of A.
I know that the RREF of A will have the bottom two rows zeroed out. But, what I don't know is where to go from here in terms of finding a matrix that satisfies the above condition.
Any help provided would be much appreciated. I'm taking an online, distance linear algebra course for credit and the materials provided are very minimal.