I returned to this today, and have a few comments. I fail to see the problem formulated as in the book. Instead of 96.5 you start from some other expression,
where, in addition, you missed the red dot (multiplication) you see inserted in this image above. The way you entered, %g_[determinant])(...) was a function, not a product, and that generated that error message about the indices (so not an index issue, the error message is correct, but an input issue in your worksheet).
In my previous reply, I suggested a step-by-step based on entering 96.5, that is
So, define your t[i,k], your h[i,k,l] as in the book, then isolate t[i,k] etc. I am not sure the steps I outlined in the previous reply will take you to 96.8, I didn't try, but if you formulate this correctly I can help you in doing that derivation in the computer.
Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft