I understand the basics of how to evaluate tensor products. For example: $$\sigma_z \otimes I = \begin{pmatrix} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & -1 & 0\\ 0 & 0 & 0 & -1\\ \end{pmatrix}$$ where $\sigma_z$ is the pauli z matrix and $I$ is the 2x2 identity.
My question arises when applying this math to two qubits. There are four operations to consider: $$1)\hspace{1cm}\sigma_z^{(1)} \otimes I^{(2)}$$ $$2)\hspace{1cm}I^{(2)} \otimes\sigma_z^{(1)}$$ $$3)\hspace{1cm}\sigma_z^{(2)} \otimes I^{(1)}$$ $$4)\hspace{1cm}I^{(1)} \otimes \sigma_z^{(2)}$$
Where the superscript denotes the qubit that the operation (gate) is applied to. So are $1)$ and $2)$ the same $4\times 4$ matrix? Or are $1)$ and $3)$ the same matrix. I guess my question can be summarized is it the order or the superscript/qubit that matters when evaluating out these tensor products into matrix form?
