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
129005 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Find the equation of the tangent to the curve y = exp(x) at the point ( a, exp(a) ). Deduce the equation of the tangent to the curve which passes through the point (0,1) .
Prove by induction that the sum of the first n integers can be written as (1/2)(n)(n+1).
The cubic equation 27(z^3) + k(z^2) + 4 = 0 has roots α, β and γ. In the case where β=γ, find the roots of the equation and determine the value of k
In statistics, what is the benefit of taking a sample survey rather than a census?