What is the determinant of -2 -3

Question

5 0

15

How you get 15

Use the definition of a determinant. From the first column you take take the element that is in the position of a permutation of 1, from the second you take the element that is in the position given by the permutation of 2. Multiply the result by the sign of the permutation and then sum over all possible permutations.

In this case the identity permutation yields zero, while the permutation that interchanges the numbers 1 and 2 yields -15. The sign of that permutation is minus one, so the result is 15.