Let A be a 2x2 matrix. Prove that there are real numbers a0, a1, ... a4, not all zero, such that

a4(A^4) + a3(A^3) + a2(A^2) + a1(A) + a0(I) = O

I've got no clue...I think it relates to basis/dimension since that is the part of the book this problem is in. But I don't know how to relate it to that.