Chapter 5.4, Problem 33E

Consider the vector space ${ℝ}^n$ with inner product $\langle x,y\rangle =x^{T}y.$ Show that for any $n\times n$ matrix A,
(a) $\langle Ax,y\rangle =\langle x,A^{T}y\rangle$
(b) $\langle A^{T}Ax,x\rangle ={\Vert Ax\Vert }^2$