Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
KatClaire
Group Title
Prove that if A is a square matrix then (A^T)^1=(A^1)^T
 one year ago
 one year ago
KatClaire Group Title
Prove that if A is a square matrix then (A^T)^1=(A^1)^T
 one year ago
 one year ago

This Question is Closed

KatClaire Group TitleBest ResponseYou've already chosen the best response.1
\[(A^{T})^{1}=(A^{1})^{T}\]
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
since A is invertible, it can be broken up into the product of two matrices \(A=XY\) combine the properties \((AB)^T=B^TA^T\) and \((AB)^{1}=B^{1}A^{1}\)
 one year ago

KatClaire Group TitleBest ResponseYou've already chosen the best response.1
This is what I wrote down, does this make sense haha \[CA^{T}=A^{T}C=I\] \[(A^{1})^{T}A^{T}=(A(A^{1}))^{T}=(AA^{1})^{T}=I^{T} = I\] and \[A^{T}(A^{1})^{T}=((A^{1})A)^{T}=(A^{1}A)^{T}= I^{T} = I\]
 one year ago

KatClaire Group TitleBest ResponseYou've already chosen the best response.1
so they both equal I
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
I guess that last part is tautological :/
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
hey, I like your way better!
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.