Let \(A\) and \(B\) be symmetric matrices of the same order. Which of the following statements is/are correct? I. \((AB - BA)\) is also a symmetric matrix. II. \((BA - AB)\) is a skew-symmetric matrix. Select the answer using the code given below.
II only
Since \(A\) and \(B\) are symmetric, \((AB-BA)^{T} = B^{T}A^{T} - A^{T}B^{T} = BA - AB = -(AB-BA)\), so \(AB-BA\) is skew-symmetric, not symmetric — statement I is false. Similarly, \((BA-AB)^{T} = AB - BA = -(BA-AB)\), so \(BA-AB\) is skew-symmetric — statement II is correct.
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