Let h: R2 ! R2 be the transformation that rotates vectors clockwise by /4 radians. (a) Find

Let h: R2 ! R2 be the transformation that rotates vectors clockwise by π/4 radians.
(a) Find the matrix H representing h with respect to the standard bases. Use Gauss's Method to reduce H to the identity.
(b) Translate the row reduction to a matrix equation TjTj-1 . . . T1H = I (the prior item shows both that H is similar to I, and that we need no column operations to derive I from H).
(c) Solve this matrix equation for H.
(d) Sketch how H is a combination of dilations, flips, skews, and projections (the identity is a trivial projection).