.Part 2 of the Fundamental Theorm of Algebra says that null space of matrix A is orthogonal to row space of A and left null space is orthogonal to column space.

Uuh? The fundamental Theorem of Algebra, as far as I know, is the one that states that the field of complex numbers is an algebraically closed field, and has nothing to do directly with matrices.

And what you want about matrices is here in "relation to the null space":

Row space - Wikipedia, the free encyclopedia

Tonio

How can one prove this?