(Solved): Question 4.6.72) Let A be an mn matrix. Prove that N(A)N(ATA). Extra: I know that this pro ...

Question 4.6.72) Let $A$ be an $m\times n$ matrix. Prove that $N(A)\subset N\left(A^{T}A\right)$. Extra: I know that this proof is on the internet, and very simple to answer once you 'get it'. Think besides the proof while doing it. What dimensions are $A^{T}A$ ? Could this show a more 'physical' reasoning behind the proof?