In a linear algebra class, we were asked to prove that a theorem is true if and only if X. (I think X may have been that a matrix had a nonzero determinant.) I

In a linear algebra class, we were asked to prove that a theorem is true if and only if X. (I think X may have been that a matrix had a nonzero determinant.) I had no idea how to do it, but I noticed the theorem was trivially true in the case of a 1x1 zero matrix. Since this matrix has a zero determinant, it spoiled the "only if" part. I wrote it as a counter-example, showing that "if AND only-if" was false, and didn't prove the "if." Full credit!