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P and A are 2x2 matrices.

 

Is the following true?

P-1AP = APP-1

Do they both simply simplify to A?

 

I had a few examples (using real matrices) that this is true. Though I'm not entirely sure since it could be some kind of luck. Interestingly I can never get:

PAP-1=AP-1P

Guest Jul 21, 2017
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 #1
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No, it is not true in general that P-1AP = APP-1.  Here is a simple counter example:

 

 

It is always true that APP-1 = A

.

Alan  Jul 21, 2017
 #2
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I see now. The maths behind matrices is abit tricky coming from algebra point of view. Thank you.

Guest Jul 21, 2017

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