The Killing form is an inner product on a finite dimensional Lie algebra g defined by
B(X,Y)=Tr(ad(X)ad(Y)) (1)
in the adjoint representation, where ad(X) is the adjoint representation of X. (1)
is adjoint-invariant in the sense that
B(ad(X)Y,Z)=-B(Y,ad(X)Z). (2)
When g is a semisimple Lie algebra, the Killing form is nondegenerate.
https://mathworld.wolfram.com/KillingForm.html