How can I show that R^2 in multiple linear regression is maximum of corr(y,Xbeta)?

Question

let $Y=X\beta +\epsilon, \ \epsilon \sim N(0,\sigma^2 I_n)$,

(Y: nx1 vector, X: nxp matrix, beta:px1 vector)

assume that both $Y$ and $X$ are centered, so that the sum of them becomes 0.

How can I show that

$R^2=1-SSE/SST=max_\beta (corr(Y,X\beta)) ^2$?

(corr is the sample correlation coefficient)

I could express $corr(Y,X\beta)=y'X\beta/\sqrt{y'y\times\beta'X'X\beta} $, but couldn't proceed.