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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 ≠ A2 + 2AB + B2
✓

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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