1. The problem statement, all variables and given/known data 1. If I got a square orthogonal matrix, then if I make up a new matrix from that by rearranging its rows, then will it also be orthogonal? 2. True/false: a square matrix is orthogonal if and only if its determinant is equal to + or - 1 2. Relevant equations no equations 3. The attempt at a solution 1. I think it should also be orthogonal since it forms a basis, and the basis would be the same, but just a linear combination of the previous, right? 2. false, its determinant doesn't necessarily ensure it is orthogonal. So, how would/should I correct that statement?