I want to understand how one can find the exterior product of square matrices. I searched about it and I find a lot of complicated formulas and without any examples. On the other hand, I found this anwser that contains a nice example. What I understood from the example is the new matrix ( I meant the exterior product one) comes from the determinant of minors of the original matrices. I want to know whether we have a similar thing for the higher-dimensional case.
Let me ask my questions better, 1) Does one can calculate the exterior product of square matrices by calculating minors of the original one? 2)Let $A$ be a $5 \times 5$ matrix. Can one give a concrete example that calculates $\wedge^3 A$? Thanks in advance