If M = [[5, 2], [3, 1]], find M⁻¹, the inverse of M.
A[[-1, 2], [3, -5]]
B[[1, -2], [-3, 5]]CORRECT
C[[1, 2], [3, 5]]
D[[-1, -2], [-3, -5]]
GCEFurther MathematicsMatrices and Determinants2021
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Why the answer is B, and why the others tempt you.
The inverse of a 2×2 matrix [[a, b], [c, d]] is (1/det) × [[d, -b], [-c, a]]. det(M) = (5)(1) - (2)(3) = 5 - 6 = -1. So M⁻¹ = (1/-1) × [[1, -2], [-3, 5]] = [[−1, 2], [3, −5]]. Wait — re-checking: (1/−1)×[[1,−2],[−3,5]] = [[−1,2],[3,−5]], which is option A. Correction: det = -1, so M⁻¹ = (-1)×[[1,-2],[-3,5]] = [[-1,2],[3,-5]], which is option A.
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