If ![A=\left[\begin{array}{cc}0&1\\1&0\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26amp%3B1%5C%5C1%26amp%3B0%5Cend%7Barray%7D%5Cright%5D "A=\left[\begin{array}{cc}0&1\\1&0\end{array}\right]")
and ![B=\left[\begin{array}{cc}1&0\\0&-1\end{array}\right]](https://tex.z-dn.net/?f=B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26amp%3B0%5C%5C0%26amp%3B-1%5Cend%7Barray%7D%5Cright%5D "B=\left[\begin{array}{cc}1&0\\0&-1\end{array}\right]")
, show that (A + B)² = A² + B².
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solve RHS and LHS seperately and we will find that both are same. A² means A×A and similarly B². fir add (A+B) to get a matrix let be C and then do C²=C×C
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