- #1

Raghav Gupta

- 1,011

- 76

## Homework Statement

If A and B are 2 matrices such that AB = A and BA =B, then B

^{2}is equal to

B

A

Zero matrix

I

## Homework Equations

We can pre or post multiply a matrix on both sides of equation.

## The Attempt at a Solution

(AB).(BA) = A.B

AB

^{2}A = A.B

Pre multiply both sides by A

^{-1}

We get B

^{2}A = AB

Implies B

^{2}

**AB**= AB as (A = AB)

Post multiplying by B

^{-1}and A we get B

^{2}= I

Is this correct?