1. If A is a square matrix satisfying , where I is the identity matrix with the same dimensions as A, does A have an inverse?
I know the answer is yes, because I found the inverse, , basically by trial and error.
But is there a more elegant/systematic way to go about this in general?
2. If A is a square matrix with determinant d, & is a number, what is the determinant of ?
I know the answer, but I don't know why it is..
Thanks for any help