I am having trouble finding the determinant in the last question.
I tried det = 15 because the first row is multiplied by 5, which multiples the original det value of 3 by 5. Then, I changed 15 into -15 because the rows are swapped.
I know that adding a scalar multiple of one row or column to another does not change the determinant. I assume if I factor out the negative sign from the last row so that it fits this rule. I end up with det = 15 again.
Where in my logic am I going awry?