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

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- May 13th 2010, 06:07 AMswiftshiftProving 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, 07:48 AMtonio

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!!

Why does this happen?? (Headbang)(Headbang)(Punch)(Angry)

Tonio - May 13th 2010, 08:08 AMundefined
- May 13th 2010, 09:09 AMtonio
- May 13th 2010, 09:13 AMtonio

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, 01:52 PMzzzoak
$\displaystyle (a+b)a^{-1}(a-b)=(a+b)(a^{-1}a-a^{-1}b)=(a+b)(I-a^{-1}b)=a+b-aa^{-1}b-ba^{-1}b=$

$\displaystyle =a-ba^{-1}b$

Please make in the same way

$\displaystyle (a-b)a^{-1}(a+b)$