 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-1/33c/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Using the rules for the matrix transpose together with

L^{T} = L

and

B^{T} = - B

[B, L]^{T} = (B L - L B)^{T} = L^{T} B^{T} - B^{T} L^{T} = - L B + B L = [B, L] .

Thus the commutator $[B, L]$ is a symmetric matrix.

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