What does it mean to “show algebraically” in propositional logic?

The biconditional operator $ \iff$ of Propositional Logic can be defined by the identity

$ p \iff q \equiv (\lnot p \lor q) \land (\lnot q \lor p) \quad (1.1)$

Use the identity $ (1.1)$ and identities from the list on page 2, to show algebraically that

$ p \iff q \equiv (\lnot p \land \lnot q) \lor (q \land p)$

State which identity you are using at each step.

What does this question mean by asking to "show algebraically"? I have tried referring to my notes and online search but no luck with a definition! These propositions are already algebraic, are they not? Having some issues understanding the wording of the question. This is from a mock university test. I’m assuming it wants me to demonstrate using a truth table?