What is the determinant of B? A. - 27 B. - 30 C. 30 D. - 6

Answer B: - 30

Step-by-step explanation:

Let B be as follows:

[-18 3]

[4 1 ]

To find the determinant, multiply diagonally downward from - 18 through 1, obtaining - 18. We keep this sign as is.

Continue: Start at 4 and move diagonally upward through 3; this product is 12. Because we moved upward, give this result the opposite sign: - 12.

Now add together these two products; that is, add together - 18 and - 12. Here the sum is - 30. This is the determinant of the matrix. It's Answer B.

Finding the determinant of a 3x3 matrix obviously requires more steps, but the general approach is similar.