$A$ is an $ \times $ matrix.
Prove that if $n < m$ then $A^{T}A$ is not invertible.

I know that when $Ax=0$ does not have trivial solution the matrix is not invertible.

So by my understanding I need to show that $x$ has a non trivial solution.

I have trouble proving this with out using dimensions and ranks since I have not yet learned those in detail.