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How to derive from the first step to the second step, where y is k by 1 vector and A is k by p matrix. Thanks for any help in advance

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Well

$(Ay - A\mu)^\top = (Ay)^\top - (A\mu)^\top = y^\top A^\top - \mu^\top A^\top = (y^\top - \mu^\top)A^\top =(y - \mu)^\top A^\top$

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