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2 Algebra questions (groups and matrices)

http://workspace.imperial.ac.uk/mathematics/public/students/ug/exampapers/2009/M2PM2-2009.PDF

How would 1(e) be done? I tried selecting two elements of A5, one with order 5 (call it x), one with order 2 (call it y) and hoped that the structure of D10 would pop out. But I couldn't get yx = x^-1 * y. So how would we proceed?

How would 3(d)(iii) be done? I can't figure out whether it is true or false. Is it just as simple as putting A^2 = I then square rooting both sides to get A = diagonal matrix with 1 or -1 in diagonals (which is obviously diagonalizable)? Or could there be other matrices that square to give I, which don't occur in this form?

Thanks for any help.