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 ${(A + B)^2} = {A^2} + 2AB + {B^2}$.
Official Solution
VVidaara Team
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NCERT & Exemplar
Since, A and B are square matrices such that $AB = BA$.
$\therefore$ ${(A + B)^2} = (A + B) \cdot (A + B)$
$= {A^2} + AB + BA + {B^2}$
$= {A^2} + AB + AB + {B^2}$
$= {A^2} + 2AB + {B^2}$
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