The matrix A = [[a, i][i, b]], where i^2 = -1, a = (1/2)(1 + sqrt(5)) and

b = (1/2)(1 - sqrt(5)) has the property that A^2 = A. Describe all 2 X 2 matrices A with complex entries such that A^2 = A.

I don't know why they give us the matrix A, as in, I don't know how to use it to solve the problem. would a method involving something like this work?

[[a, b][c, d]] [[a, b][c, d]] = [[a, b][c, d]]

and try to solve for a, b, c, d?

BTW, the answer is this:

[[a, b][c, 1-a]], where b and c are arbitrary and a is any solution of the quadratic equation a^2 - a + bc = 0.