I have been doing some practice problems from "Gentle introduction to Quantum Computing". I am a little bit lost with this one:

The generalized Pauli group $\mathcal G_n$ is defined by all elements of $\mathcal G_n$ being of the form $\mu A_1\otimes A_2 \otimes \ldots\otimes A_n$ where $A_j\in\left\lbrace I, X, Y, Z\right\rbrace$ and $\mu\in\left\lbrace 1, i, -1, -i\right\rbrace$.

Show that generalized set of Pauli elements for a basis for the linear transformations on the vector space associated with an n-qubit system.

Is there any formal proof for this problem? And how do I approach it?

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    $\begingroup$ +1. But what is meant here by "THE generalized set of Pauli elements"? $\endgroup$ – user1271772 May 29 '20 at 21:39