Proving Similarity of Matrices with Scalar x: A-xI and B-xI

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If A and B are similar matrices, then show that A-xI and B-xI are similar were x is a scalar.

How to start?
 
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Dustinsfl said:
If A and B are similar matrices, then show that A-xI and B-xI are similar were x is a scalar.

How to start?
Since A and B are similar, you know that A = P-1BP.

Then A - xI = P-1BP - xI = P-1BP -Ix. (You can multiply by a constant on the right or the left).

If you work with this maybe you can end up with what you need to show that A - xI is similar to B - xI.
 
If we have this line A - xI = P-1BP - xI, can't I just add xI from the left to right?
 
I'm not sure what you're asking. xI and Ix are equal. In general, cA = Ac, where c is a scalar and A is a matrix.

I wrote it the way I did for a reason, though.
 

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