Suppose that the real matrices A and B are orthogonally diagonalizable and AB=BA. Show that AB is orthogonally diagonalizable.(adsbygoogle = window.adsbygoogle || []).push({});

I know that orthogonally diagonalizable means that you can find an orthogonal matrix Q and a Diagonal matrix D so Q^TAQ=D, A=QDQ^T.

I am aware of the Real Spectral Theorem which states that "A real (mxn)-matrix A is orthogonally diagonalizable if and only if A is symmetric"

I got a hint saying I am suppose to use the Real Spectral Theorem twice to show it. But I am still unsure as to how to do this.

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# Showing it is orthogonally diagonalizable

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