Fewpal
0 votes
4 views
ago in Matrices by (46.2k points)
closed ago by

If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal to

A. A
B. I – A
C. I + A
D. 3A

1 Answer

+1 vote
ago by (24k points)
selected ago by
 
Best answer

As, (A – I)3 + (A + I)3

Use a3 + b3 = (a + b)(a2 + ab + b2)

Also A2 = I

∴ then (A – I)3 + (A + I)3 – 7A = 2A + 6A – 7A = A

Clearly our answer matches with option (A)

∴ Option (A) is the correct answer.

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.

...