Statistics problem

[SirVLCIV]

I'm taking a course (not the VEE exam), but I've been having difficulty on this.

What's the variance of S^2=(1/n)*Sum(Xi-Xbar)^2?

s^2=(1/(n-1))*Sum(Xi-Xbar)^2 is the sample variance and is chi-square with n-1 degrees of freedom, no? Or am I screwing something up?

[SirVLCIV]

Nevermind, I got it: Sum(Xi-Xbar)^2/sigma^2 is chi-squared with n-1 degrees of freedom, which solves it (variance of Chi-square is 2*df), then multiply by ((sigma^2)/(n))^2