Matrices — Class 12 Maths Solution

exemplar sa SA NCERT,Exemp,Q.no.31,Page 56
Question

Show that, if A and B are square matrices such that $AB = BA$, then ${(A + B)^2} = {A^2} + 2AB + {B^2}$.

Step-by-step Solution

Since, A and B are square matrices such that $AB = BA$.

$\therefore$ ${(A + B)^2} = (A + B) \cdot (A + B)$

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

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

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Matrices. Curated by Sachin Sharma. Free for all students.