How to calculate matrix tr(AB)

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I have these Matrix A and B below in the image:

And i wonder how do i calculate the tr(AB)? I have done this by taking the diagonal in each Matrix A and B:

3 * 6 + 1 * 5 + 5 * 9 = 67

But after that i get stuck i have tried to search for an answer but i couldn't find any thing that explained that?

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1 Answer

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You can read about the list of properties of trace of a matrix - here.

Now, in this problem, you have to find $AB$ first, but explicitly evaluating the matrix product and then sum the diagonal elements. There no other easier way about it.

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