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
128327 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸'Find the first derivative, with respect to x, of arctan(1/x) for non-zero real x. Hence show that the value of arctan(x)+arctan(1/x) is constant for all non-zero x, explicitly stating this constant in your final answer.' How do I solve this?
The curve C has parametric equations x=cos(t)+1/2*sin(2t) and y =-(1+sin(t)) for 0<=t<=2π. Find a Cartesian equation for C. Find the volume of the solid of revolution of C about the y-axis.
The plane Π contains the points (1, 2, 3), (0, 1, 2) and (2, 3, 0). What is the vector equation of the plane? and what is the cartesian equation of the plane?
Prove by induction the sum of n consecutive positive integers is of the form n(n+1)/2.