All about
flooble

fun stuff

Get a free chatterbox

Free JavaScript

Avatars
perplexus
dot
info
Home
>
Just Math
Matrix Mathematics (
Posted on 20161030
)
Suppose
A
and
B
are two non singular matrices such that
AB = BA^2
and
B^5 = I
, then prove that
A^31= I
Note:
Here
I
is the identity matrix.
No Solution Yet
Submitted by
Danish Ahmed Khan
No Rating
Comments: (
Back to comment list
 You must be logged in to post comments.
)
Solution
Comment 1 of 1
Let B' denote the inverse of B. Then B^5=I implies B'^5=I.
Rearrange A*B=B*A^2 into
A = B*A^2*B'
Then substitute the latter equation into itself to get
A = B^2*A^4*B'^2
Substitute three more times to get the series of equations
A = B^3*A^8*B'^3
A = B^4*A^16*B'^4
A = B^5*A^32*B'^5
The last one simplifies to I = A^31.
Posted by
Brian Smith
on 20161030 10:07:00
Please log in:
Login:
Password:
Remember me:
Sign up!

Forgot password
Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ

About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On
Chatterbox:
blackjack
flooble's webmaster puzzle
Copyright © 2002  2018 by
Animus Pactum Consulting
. All rights reserved.
Privacy Information