Let M and N be two 3x3 non-singular skew-symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2(MTN)T(MN)T is equal to?

Let M and N be two 3x3 non-singular skew-symmetric matrices such that MN = NM.
Since M and N are skew-symmetric, we have MT = -M and NT = -N.
We are given the expression M2N2(MTN)T(MN)T.
We can rewrite this as:
M2N2(NTMT)(NTMT) = M2N2((-N)(-M)) = M2N2(NM)
Since MN = NM, we have:
M2N2(NM) = M2N2(MN) = M2N(NMN) = M2N(MNM) = M3N2M
However, this does not simplify to any of the given options. Let's use the properties of skew-symmetric matrices and the given condition MN = NM.
Consider the expression M2N2(MTN)T(MN)T.
We have (MTN)T = NTMT = (-N)(-M) = NM and (MN)T = NTMT = (-N)(-M) = NM.
Therefore, the expression becomes:
M2N2(NM)(NM) = M2N2(NM)2 = M2N2(N2M2) = M2N4M2
Since MN = NM, we can write M2N2(MTN)T(MN)T = M2N2(NM)(NM) = M2N2(MN)(MN) = M2N2M2N2 = M4N4
Let's use the property that for a skew-symmetric matrix A, A2 is symmetric. Thus, M2 and N2 are symmetric.
Also, (AB)T = BTAT. So (MTN)T = NTMT = (-N)(-M) = NM.
Similarly, (MN)T = NTMT = (-N)(-M) = NM.
So we have M2N2(NM)(NM) = M2N2(NM)2 = M2N2N2M2 = M2N4M2
Since M2 and N2 are symmetric, and they commute (MN = NM implies M2N2 = N2M2), we can't directly simplify to any of the options. There might be an error in the question or options provided.