Please solve ...Thank you

Problem 1. Consider the inner product on R2 given by (v, w) = [01 02] 1 2 W1 -1 W/2 (You do not need to show that this is an inner product) (a) Let A E 2 (R?) be the operator defined by A(x, y) = (-y, x). Show that A is normal with respect to the dot product on R', but not normal with respect to (-; -). Hint: Show that set {(1, 0), (1, 1) } is an orthonormal basis of R with respect to (-, -). (b) Explain why A is not self-adjoint with respect to any inner product on R2