Thread: Powers of matrices. Geometric interpretation.

Q is in 2x2 matrix form, Q= (0, -1, 1, 0)
Using geometrical reasoning only, state the smallest possible values of k given that:

a)Q^-1=Q^k
Q^-1=Q^3

b) Q^5=Q^k
Q^%=Q^1

c) Q^2=Q^k
Q^-2=Q^2

See, I know how to get the answer, I just don't know how to explain it using geometrical reasoning.

Think of Q as a rotation. How many of these rotations are required to get back to where you started? After that, it's just modular arithmetic.

you can also think of Q as a multiplication by a certain complex number. which complex number? well, what is Q^2?