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May 15th, 2017, 06:51 PM   #1
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$a^2 = -I $

Let $\displaystyle A \epsilon M_n(R) $. If $A^2 = -I $ (where $I$ is the Identity matrix), then
A) $n$ is even.
B) $A= +$ or $- I$
C) all eigenvalues of $A$ are in $R$.
D) $A$ is a diagonal matrix.
Please explain this with an example if possible.
Thank you so much.

Last edited by skipjack; May 19th, 2017 at 07:49 AM.
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May 17th, 2017, 10:23 PM   #2
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Quote:
Originally Posted by Lalitha183 View Post
Let $\displaystyle A \epsilon M_n(R) $. If $A^2 = -I $ (where $I$ is the Identity matrix), then
A) $n$ is even.
B) $A= +$ or $- I$
C) all eigenvalues of $A$ are in $R$.
D) $A$ is a diagonal matrix.
Please explain this with an example if possible.
Thank you so much.
Please someone help!
Thank you

Last edited by skipjack; May 19th, 2017 at 07:49 AM.
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May 18th, 2017, 08:08 AM   #3
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The only true statement is A.

Thanks from zylo
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May 18th, 2017, 08:25 AM   #4
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Quote:
Originally Posted by johng40 View Post
The only true statement is A.

Thank you for your clear explanation
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May 19th, 2017, 07:43 AM   #5
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(A$\displaystyle ^{2}$=-I)A$\displaystyle ^{-1}$ $\displaystyle \rightarrow$ A$\displaystyle ^{-1}$=-A

Last edited by skipjack; May 19th, 2017 at 07:52 AM.
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May 19th, 2017, 09:11 AM   #6
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Originally Posted by zylo View Post
(A$\displaystyle ^{2}$=-I)A$\displaystyle ^{-1}$ $\displaystyle \rightarrow$ A$\displaystyle ^{-1}$=-A
The above is generally not true, but it can be true, as johng40 points out, and the question is IF A^{2}=-I then.....

My apologies to johng40 and Lalitha183.

Just out of curiosity, what did skipjack edit in above post?
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