If A and B are two matrices and (A + B)(A - B) = {A^2} - {B^2} , then

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3 and 4 .Determinants and Matrices

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If $A$ and $B$ are two matrices and $(A + B)(A - B)$$ = {A^2} - {B^2}$, then

A

$AB = BA$

B

${A^2} + {B^2} = {A^2} - {B^2}$

C

$A'B' = AB$

D

None of these

Solution

(a) Since $(A + B)(A – B) = {A^2} – {B^2}$

By matrix distribution law,

==> ${A^2} – AB + BA – {B^2} = {A^2} – {B^2}$

==> $BA – AB = 0\,\, \Rightarrow BA = AB$.

Standard 12

Mathematics

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