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  • Show that if A and B are square matrices such that AB = BA, then (A + B)^2 = A^2 + 2AB + B^2.

Show that if A and B are square matrices such that AB = BA, then (A + B)^2 = A^2 + 2AB + B^2.

 

Answers (1)

According to matrix multiplication we can say that:

(A + B)\textsuperscript{2} = (A+B)(A+B) = A\textsuperscript{2} + AB + BA + B\textsuperscript{2}

We know that matrix multiplication is not commutative but it is given that: AB = BA

\therefore (A + B)^{2} = A^{2} + AB + AB + B^{2} \\ \Rightarrow (A + B)^{2} = A^{2} + 2AB + B^{2} \ldots is proved

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infoexpert22

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