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Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
Let $A$ and $B$ be square matrices of the same order. Does $(A+B)^2=A^2+2 A B+B^2$ hold? If not, why?
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Answer

$L H S=(A+B)^2$
$=(A+B)(A+B)$
$=A(A+B)+B(A+B)$
$=A^2+A B+B A+B^2$
We know that a matrix does not have commutative property. So,
$A B \neq B A$
Thus,
$(A+B)^2 \neq A^2+2 A B+B^2$

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