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Looking for a way to create a particular matrix in python in a less amount of time

Solving the matrix equation $X^tA+A^tX=0$ for $X$ in terms of $A$

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Randomly permute $\{1,\cdots,100\}$. What is the probability that none of the $S_k$'s defined by $\sigma(1)+\cdots+\sigma(k)$ is divisible by $3$?