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Use the inverse of a 2x2 matrix formula to confirm that: "The product of two symmetric matrices is symmetric if and only if the matrices commute." IN THE CASE where the symmetric matrix $\begin{pmatrix} a & b \\ b & d \end{pmatrix}$ is invertible.

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  • $\begingroup$ Answer to a related question from a year later. $\endgroup$
    – PinkyWay
    Aug 30, 2020 at 13:31

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$$(AB)^t=B^tA^t\implies \left((AB)^t=AB\iff BA=B^tA^t=AB\right)$$

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  • $\begingroup$ What is the link with the inverse? What are you exactly saying? Sorry, I'm bad in math. $\endgroup$
    – yolo123
    Jul 5, 2014 at 10:12
  • $\begingroup$ This is a proof which doesn't use the inverse of a $2\times2$ matrix, in fact it's a proof that works for square matrices of any size, invertible or not. $\endgroup$ Jul 5, 2014 at 10:45

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