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Algebra Level 3

If $$\color{red}{A}$$ and $$\color{blue}{B}$$ are two non-singular matrices such that $$\color{red}{A}\color{blue}{B}$$ = $$\color{blue}{B}$$ and $$\color{blue}{B}\color{red}{A}$$ = $$\color{blue}{A}$$,then.

$\large \color{red}{A^2} + \color{blue}{B^2} =$

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