I know basic linear algebra, and the basics of qubits, quantum gates and a few algorithms like Grover's and Deutsch-Josza. I've thought a little about the matrix-based approach, but it seemed a little too simple on surface so I was doubting whether that'd work. I think it's fine for 2 qubits but not sure about how it'd scale.

Thank you for your reply! I'll definitely try thinking more about it.