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P and Q are different matrices that are 2x2. I have tried to do this by letting both equal a 'made-up' matrix with pro numerals, but the expansion process is very long. Is there an easy way to simplify this?

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    $\begingroup$ It is $2PQ+2QP$ $\endgroup$ – Kavi Rama Murthy Aug 13 at 8:57
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Hint:

$$(P+Q)^2=(P+Q)(P+Q) = P\cdot P + P\cdot Q + Q\cdot P + Q\cdot Q$$

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  • $\begingroup$ I tried to use the difference of squares method and ended up realising that matrix multiplication is not commutative, so I gave up on expanding the P's and Q's. Thanks for reminding me about other ways to go about this! $\endgroup$ – Donkey Kong Aug 13 at 9:20

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