The determinant of a 2x2 matrix [a b; c d] with a=3, b=4, c=2, d=5 is computed as ad - bc. Which value is correct?

The determinant of a 2x2 matrix [a b; c d] with a=3, b=4, c=2, d=5 is computed as ad - bc. Which value is correct?

• A. -7
• B. 7
• C. 1
• D. 3

Answer: (B)

The determinant of a 2x2 matrix is found by multiplying the top-left and bottom-right entries and then subtracting the product of the top-right and bottom-left entries. With a = 3, b = 4, c = 2, d = 5, compute ad = 3×5 = 15 and bc = 4×2 = 8. Subtract to get ad − bc = 15 − 8 = 7. So the determinant is 7. This result comes directly from the standard formula for a 2x2 determinant and reflects using the diagonals in the subtraction. If you see -7, that would come from reversing the order (bc − ad). The values 1 or 3 would come from different arithmetic outcomes.

The determinant of a 2x2 matrix is found by multiplying the top-left and bottom-right entries and then subtracting the product of the top-right and bottom-left entries. With a = 3, b = 4, c = 2, d = 5, compute ad = 3×5 = 15 and bc = 4×2 = 8. Subtract to get ad − bc = 15 − 8 = 7. So the determinant is 7. This result comes directly from the standard formula for a 2x2 determinant and reflects using the diagonals in the subtraction. If you see -7, that would come from reversing the order (bc − ad). The values 1 or 3 would come from different arithmetic outcomes.