Greetings! I'm trying to prove that detA = detA^T by showing that detE = detE^T. I'm not sure how to prove that detE = detE^T, where E is an elementary matrix and that E^T is the transpose of E. I plan to approach this by taking the determinant of a generic elementary matrix, for each type of elementary matrix (row swap, scale, and combining rows). Is there a faster/better way to do this? Thanks!