Note that without the non-linear part each layer would just be a single linear map. The composition of multiple layers would then be a linear map again, so there would be no need for multiple layers in a model.
It matters, because this sub isn't to answer homework questions.
I asked, because the way you asked somehow gave me the exact vibes I get when my students ask me questions when they are trying to get me to solve the problem for them.
hjmb t1_irzxltz wrote
No - layers in neural networks are often a linear map followed by component-wise non-linear maps. The resulting operation is non-linear.