Well, I know this question can be a little bit stupid. But, still... a neural network is a several linear transormations $L_1,\ldots, L_m$ that are sequentialy appilied to feature vector $X$. A compositon of linear transformations is a linear transformation. So after all we get $L X$ where $L$ is a composition of $L_1,\ldots, L_m$.
The question is: if eventually we have that neural network is just applying a liner transformation to a feature vector what is the essential difference betwen neural networks and linear regression