What makes multi-layer neural networks able to perform nonlinear operations? As I know, a single layer neural network can only do linear operations, but multilayered ones can.

Also, I recently learned that finite matrices/tensors, which are used in many neural networks, can only represent linear operations.

However, multi-layered neural networks can represent non-linear (even much more complex than being just a nonlinear) operations.

What makes it happen? The activation layer?
Nonlinear relations between input and output can be achieved by using a nonlinear activation function on the value of each neuron, before it's passed on to the neurons in the next layer.