(a) We have, A^{2} = I

Also A and I are commutative, so we can expand (A+I)^{n} using expansion of (a+b)^{n}, where a and b ∈ C

∴ (A-I)^{3} + (A+I)^{3} - 7A

= A^{3} - 3A^{2} + 3A - I3 + A^{3} + 3A^{2} + 3A + I^{3} - 7A

= 2A^{3} + 6A - 7A

= 2A^{2} . A + 6A - 7A

= 2I.A + 6A - 7A

= 2A + 6A - 7A = 8A - 7A = A