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Matrices

The non singular matrices A and B are such that AB=BA and ABA=B


Prove that A^2 =I

I don’t understand the working of the answer. I’ll post a pic
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MM2002
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image.jpgI don’t understand how The a squared term was gained in second arrow ??Thanks for any replies
Original post by MM2002
The non singular matrices A and B are such that AB=BA and ABA=B


Prove that A^2 =I

I don’t understand the working of the answer. I’ll post a pic


If B = ABA then what do you get when you multiply by A?
Original post by MM2002
I don’t understand how The a squared term was gained in second arrow ??Thanks for any replies

Multiplication of matrices is associative so A(AB) is equal to (AA)B, hence A²B.
Original post by MarkFromWales
Multiplication of matrices is associative so A(AB) is equal to (AA)B, hence A²B.

And A^2BB^-1=BB^-1

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