Find the determinant of upper triangular matrices (where $a_{ij}=0$ when $i>j$).
I am not sure how to calculate this using the definition of a determinant. It is the bit with the permutations '$σ$' that doesn't make any sense.
If someone could provide the solution to this problem with an explanation of the permutations $( σ)$ it would help very much.
$$\det (A) = \sum\limits_{\sigma \in {S_n}} {{\mathop{\rm sgn}} (\sigma ){a_{\sigma (1),1}}...{a_{\sigma (n),n}}} $$