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
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Answered by Katie H. • Further Mathematics tutor
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