Determinant of a scaled product

A and B are 3×3 matrices with det(A)=3 and det(B)=4. Compute det(2A·B⁻¹).

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For an $n\times n$ matrix, $\det(cA) = c^n\det(A)$ - here $\det(2A) = 2^3\cdot 3 = 24$ .
$\det(B^{-1}) = 1/\det(B)$ ; combine multiplicatively: $24 \cdot \tfrac14 = 6$ .

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Asked at: Probability & Market-Making, Data-Driven Research