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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If A and B are square matrices of the same order, explain, why in general:
$(A + B)^2 \neq A^2 + 2AB + B^2$
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Answer

$\text { LHS }=(A+B)^2$
$=(A+B)(A+B)$
$=A(A+B)+B(A+B)$
$=A^2+A B+B A+B^2$
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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