﻿ Let A, B be two n × n matrix such that A + B = AB, then : Kaysons Education

# Let A, B be Two n × n matrix Such That A + B = AB, Then

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### Solution

Correct option is

AB = BA

A + B = AB  ⇒ In – A – B + AB = In

Thus, AB = A + B = B + A = BA.

#### SIMILAR QUESTIONS

Q1

, then value of α for which A2 = B is

Q2
Q3
Q4

Let A and B be two 2 × 2 matrices. Consider the statements

(i) AB = O ⇒ A = O or B = O

(ii) AB = I2 ⇒ A = B–1

(iii) (A + B)2 = A2 + 2AB + B2.

Then

Q5

If A and B are symmetric matrices, then AB – BA is a

Q6

The inverse of a symmetric matrix (if it exists) is

Q7

The inverse of a skew symmetric matrix (if it exists) is

Q8

The inverse of a skew symmetric matrix of odd order is

Q9

If A is an orthogonal matrix, then |A| is

Q10

If A is a non-singular matrix of size 3 × 3, then adj (adj A) is equal to