How Does Variation in the Metric Determinant Depend on Its Inverse?

[Themetricsystem]

Let h = det h_{alpha beta}. The number of dimensions is not necessarily four. Show that
$$\[<br /> \delta h = -h h_{\alpha \beta} \delta h^{\alpha \beta} \, ;<br /> \]$$

delta h is the variation in h.

Not sure how to start.

 

[dextercioby]

HINT:

$$\mbox{det} A=\exp\mbox{Tr} \ \ln A$$

Daniel.