Edit: I don't think this is a duplicate. That question is generally about efficient algorithms for calculating the determinant. While my question is about practical tips and tricks which can be used when doing this sort of thing by hand.
During one of the questions I was solving I came across the following determinant:
I solved it directly by expanding from the third column and got the result $(t-1)^4$.
However, along the way I made a couple of calculation errors and finding them took me a while. This got me thinking that maybe there are some tips and tricks I could use to calculate this in a faster less error prone method. Or maybe, at least know that I got the right answer in some way?
Any tips that could interest me?