0 votes
in Matrices by (49.6k points)
closed by

Show that if A and B are square matrices such that AB = BA, then (A + B)2 = A2 + 2AB + B2.

1 Answer

+1 vote
by (29.2k points)
selected by
Best answer

By matrix multiplication we can write:

(A + B)2 = (A+B)(A+B) = A2 + AB + BA + B2

We know that matrix multiplication is not commutative but it is given that : AB = BA

∴ (A + B)2 = A2 + AB + AB + B2

⇒ (A + B)2 = A2 + 2AB + B2 …proved

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.