My government has told me that I must teach 17 year olds how to invert a 3 by 3 matrix using adjoints/cofactors, without using any technology.
Is there any reason why you would want to know how to do this by hand? (As opposed to on calculator)
When we went through the step-by-step recipe ("And now, you change the signs of these entries...") the students wanted to know why it works. I am loath to hand over a magic recipe without justifying, but am unsure of what to say. What could I say?