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  4. If A and B are square matrices of the same order, then (A + B)2 = A2 + 2AB + B2 implies

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Q. If A and B are square matrices of the same order, then $(A + B)^2 = A^2 + 2AB + B^2$ implies

Matrices

Solution:

$\left(A + B\right)^{2} =A^{2} +2AB +B^{2} $
$ \Rightarrow \left(A + B\right)\left(A + B\right) = A^{2} + 2AB + B^{2} $
$ \Rightarrow A^{2} + AB + BA +B^{2 } = A^{2 } + 2AB + B^{2} $
$\Rightarrow BA = AB$