 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-1/5a/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Both sides are antisymmetric in

j, k

and in

p, q

. If either pair has equal indices, both sides vanish. It therefore suffices to take

j \neq = k

and

p \neq = q

. The sum over

i

is nonzero exactly when

(p, q) = (j, k)

(k, j)

; it is respectively

1

- 1

. This is exactly

ϵ_{ijk} ϵ_{i pq} = δ_{j p} δ_{k q} - δ_{j q} δ_{k p},

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