The determinant of A = [[1,2],[3,4]] is -2. Which statement is true about det(A)?

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The determinant of A = [[1,2],[3,4]] is -2. Which statement is true about det(A)?

The key idea is how to compute a determinant of a 2×2 matrix. For a matrix [[a, b], [c, d]] the determinant is ad − bc. Here a = 1, b = 2, c = 3, d = 4, so det(A) = 1×4 − 2×3 = 4 − 6 = −2. That makes the statement det(A) equals −2 true. The other numbers would require different arithmetic: 0 would need ad = bc (which is not the case here), 2 would require ad − bc = 2 (not true here), and −4 would need ad − bc = −4 (also not true).

The key idea is how to compute a determinant of a 2×2 matrix. For a matrix [[a, b], [c, d]] the determinant is ad − bc. Here a = 1, b = 2, c = 3, d = 4, so det(A) = 1×4 − 2×3 = 4 − 6 = −2. That makes the statement det(A) equals −2 true. The other numbers would require different arithmetic: 0 would need ad = bc (which is not the case here), 2 would require ad − bc = 2 (not true here), and −4 would need ad − bc = −4 (also not true).

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