What is the || and * operator mean when referring to matrices?

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I have the following matrix equation,

$$ Ap || E ==> p || A^* E $$

What does || and * mean in this context, where A is a n x n matrix, p is a n x 1 matrix, and E is also an n x 1 matrix.

The context is from a Game Theory question revovling around ESS. It is as described below,

For the following symmetric games [A,A^T], find all symmetric equilibrium pairs which use all the pure strategies i.e. find all SE of the form <p,p>, pi>0 for all i, Which of these are ESS?

And in order to find ESS, the steps are as follows,

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