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
KH
Answered by Katie H. • Further Mathematics tutor
128500 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Integrate (4x+3)^1/2 with respect to x.
Use de Moivre’s theorem to show that, (sin(x))^5 = A sin(5x) + Bsin(3x) + Csin(x), where A , B and C are constants to be found.
Solve the differential equations dx/dt=2x+y+1 and dy/dt=4x-y+1 given that when t=0 x=20 and y=60. (A2 Further pure)
Integrate x^2sin(x) between -pi and pi