Anyone good with index notation and vector calculus?

| δ[ir] δ[is] δ[ik] |
| δ[jr] δ[js] δ[jk] |
| δ[kr] δ[ks] δ[kk] |

+δ[ir].
| δ[js] δ[jk] |
| δ[ks] 1.... |
- δ[is].
| δ[jr] δ[jk] |
| δ[kr] 1.... |
+ δ[ik].
| δ[jr] δ[js] |
| δ[kr] δ[ks] |


δ[ir].δ[js] - δ[ir].δ[jk].δ[ks]
- δ[is].δ[jr] + δ[is].δ[jk].δ[kr]
+ δ[ik].δ[jr].δ[ks] - δ[ik].δ[js].δ[kr]
I guess you wnt wrong just expanding the determinant? I'm pretty sure this is right.

edit: no code tags?