Answers>Further Mathematics>A Level>Article

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^-1post 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

Answered by Katie H. • Further Mathematics tutor

129003 Views

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

Related Further Mathematics A Level answers

using an integrating factor, find the general solution of the differential equation dy/dx +y(tanx)=tan^3(x)sec(x)

How do I convert cartesian coordinates into polar coordinates?

What are the different forms of complex numbers and how do you convert between them?

How do I use proof by induction?