# Proving that matrices commute

• May 13th 2010, 07:07 AM
swiftshift
Proving that matrices commute
1) A and B are n x n matrices and A is invertible. Show that
(A+B)A^-1(A-B) = (A-B)A^-1(A+B)

2) A and B are n x n invertible matrices that commute. Show that A^-1 and B^-1 also commute
• May 13th 2010, 08:48 AM
tonio
Quote:

Originally Posted by swiftshift
1) A and B are n x n matrices and A is invertible. Show that
(A+B)A^-1(A-B) = (A-B)A^-1(A+B)

2) A and B are n x n invertible matrices that commute. Show that A^-1 and B^-1 also commute

This is annoying! Sorry, but already 5(!!!) times I tried to answer this question and each darn time I click on "Preview" all the *#&\$*# letters of my response, and the question's too, are changed into non-capital letters, whne I typed them all capital!!

Tonio
• May 13th 2010, 09:08 AM
undefined
Quote:

Originally Posted by tonio
This is annoying! Sorry, but already 5(!!!) times I tried to answer this question and each darn time I click on "Preview" all the *#&\$*# letters of my response, and the question's too, are changed into non-capital letters, whne I typed them all capital!!

Tonio

That's never happened to me before. Have you tried a browser restart?
• May 13th 2010, 10:09 AM
tonio
Quote:

Originally Posted by swiftshift
1) a and b are n x n matrices and a is invertible. Show that
(a+b)a^-1(a-b) = (a-b)a^-1(a+b)

2) a and b are n x n invertible matrices that commute. Show that a^-1 and b^-1 also commute

$(a+b)a^{-1}(a-b)=(a+b)(i-a^{-1}b)$
• May 13th 2010, 10:13 AM
tonio
Quote:

Originally Posted by undefined
That's never happened to me before. Have you tried a browser restart?

Well, as you can see below it didn't work...I hope some of the bosses of the forum can help me(us) out of this annoying phenomenum, which I've never, ever met before.

This time (below) I sent the post's beginning hoping that upon sending, against merely "previewing", it will show correct, which it obviously didn't...and I not only restarted my browser: I am now writing from Modzilla, whereas I always uses Explorer...!

I'm afraid either my computer has a virus (a rather peculiar one), or else this particular post is hexed, or else the forum is stoned and doing nonsenses.

**sigh**

Tonio
• May 13th 2010, 02:52 PM
zzzoak
$(a+b)a^{-1}(a-b)=(a+b)(a^{-1}a-a^{-1}b)=(a+b)(I-a^{-1}b)=a+b-aa^{-1}b-ba^{-1}b=$
$=a-ba^{-1}b$
Please make in the same way
$(a-b)a^{-1}(a+b)$