My point was not to say that familiarity with the determinant formula was worthless. Potentially, with an infinite amount of time and scratch paper, etc., doin

My point was not to say that familiarity with the determinant formula was worthless. Potentially, with an infinite amount of time and scratch paper, etc., doing the determinant of one 6x6 in a homework setting might be a worthwhile activity. However, presenting a nonzero nonsparse 6x6 as a "break" between two formal proofs on a large timed exam is not my idea of the level of arithmetic agility that should be expected of an undergrad CS student. No doubt there are great insights to be gained from application of the determinant formula. One that occurred to me at the time was "Computationally, what is the best order to perform these operations to get a numerically exact result? What is the time complexity of a perfect algorithm to determine the best-exact order? Is there a faster approximation that still provides good results?" etc. Unfortunately, I never pursued any of these arguably-more-relevant questions, because I was busy getting my rote multiplication up to speed. I never even thought of some of your applications, because I was too busy with nonsense to make connections. While this is a point example, it in many ways is representative of my math education.