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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:
$(A + B)(A - B) \neq A^2 - B^2.$
✓

Answer

LHS $= (A + B)(A - B)$
$= A(A - B) + B(A - B)$
$= A^2 - AB + BA - B^2$
We know that a matrix does not have commutative property. So,
$AB ≠ BA$
Thus,
$(A + B)(A - B) \neq A^2 - B^2$

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