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Let A and B be two 2x2 non-singular skew-symmetric matrices such that AB = BA. If P^T denotes the transpose of matrix P, then the value of (B² A²)² * ((B^T A^(-1))² * (B A^(-1))^T)² is equal to:

1. A⁴
2. B⁴
3. A²
4. A² B²

Correct answer: B⁴

Solution

Using the properties of 2x2 skew-symmetric matrices (A^T=-A, A²=-det(A)*I, A^(-1)=-A/det(A)) and AB=BA, each factor can be expressed as a scalar multiple of the identity, and the final expression simplifies to det(B)²*det(A)²*I scaled in a way that matches B⁴ = det(B)²*I.

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