I've been asked to compute the determinant of a $3 \times 3$ matrix with complex entries. I have done so using the normal expansion along a row or column method that I would use were the entries real. My questions are:
1) is this what I should be doing?
2) I obtained a complex result - how do I interpret what this means? I've been given to understand that the absolute of the determinant of a $3 \times 3$ matrix would represent it's volume, but can a volume be complex?