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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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