Does EAE^(-1) equal E^(-1)AE for matrices?

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Thread starter Woolyabyss
Start date Nov 21, 2014

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Woolyabyss

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Nov 21, 2014

I know that matrix and its inverse are commutative i.e. E*E^(-1) = E^(-1)*E

but is a matrix and its inverse at either side of another matrix commutative?
E*A*E^(-1) = E^(-1)*A*E

Any help would be appreciated.

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Nov 21, 2014

Not in general.
Otherwise every coordinate transformation would be equivalent to its inverse transformation.

Does E*A*E^(-1) equal E^(-1)*A*E for matrices?

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