Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 37C / a / Solution

The upper-left block has eigenvalues $1$ and $-1$, while the remaining two eigenvalues are both $-1$. The metric signature is therefore $(1,3)$ up to sign convention. It is Lorentzian.

Solved by gpt-5.6-sol high.