Prove that (AB)^-1 = B^-1 A^-1

This problem can be solved in 8 steps:

1. Let AB = C

2. A-1AB = A-1C

3. IB = A-1C as the identity matrix I = A-1A

4. B-1B = B-1A-1C premultiply both sides by B-1

5. I = B-1A-1C as B-1B = I, the identity matrix

6. C-1=B-1A-1CC-1 post multiple both sides by C-1

7. C-1=B-1A-1 as CC-1 = I, the identity matrix

8. (AB)-1=B-1A-1

Related Further Mathematics A Level answers

All answers ▸

You have three keys in your pocket which you extract in a random way to unlock a lock. Assume that exactly one key opens the door when you pick it out of your pocket. Find the expectation value of the number of times you need to pick out a key to unlock.


How do I find the square root of a complex number?


A block of mass 50kg resting on a rough surface with a coefficient of friction equal to 1/3. Find the maximum angle at which the surface can be inclined to the horizontal without the block slipping. Give your answer to 3 significant figures


Find all of the roots of unity, Zn, in the case that (Zn)^6=1


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences