Determine values for a so that function is strictly convex/concave/indefinite?

I am given a function:

g(x,y,z) = ax^2 - y^2 + xy - z^2

The full question is:

Determine for which (if any) values of a is g (x, y, z) strictly concave, for which (if any) it is strictly convex, and for which (if any) it is indefinite.

I know how to find D^2 but I am struggling to remember how to go about find values for a, I did this in a revision lecture but the lecture slides don't give the workings, he did that on the board and I cannot find my notes on it. :(

Any help much appreciated as always MHF.

Regards,
Wevans2303.