Thank you both for your replies, but I too do not think the determinant is what the prof is looking for. For some context, I am not looking for actual answers to the problems, once I figure out what the prof wants I intend to do all the math myself! I'm freshly back in the classroom after...
I have a metric given as a line element differential ds^2. I have written down the 3x3 matrix with the coefficients. I am then asked to determine "g" (which I think i just did by enumerating the matrix) and "g^ij", which I normally would assume means the same thing, but apparently not.
So...