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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
Let A and B be square matrices of the same order. Does (A + B)2 = A2 + 2AB + B2 hold? If not, why?
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Answer

LHS = (A + B)2
= (A + B)(A + B)
= A(A + B) + B(A + B)
= A2 + AB + BA + B2
We know that a matrix does not have commutative property. So,
AB ≠ BA
Thus,
(A + B)2 ≠ A2 + 2AB + B2

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