The Attempt at a Solution
For a) I just solved simultaneous equations, a link to a resource that solves a system more efficiently would be nice but augmented matrices are taught in the syllabus, or atleast not in the official text. Although I've seen solutions in the mark schemes of augmented matrices.
Next I get the determinent in terms of a, a=1 when determinent is 0.
I'm not sure how to do this last part.