A doubt

[vishak h pillai]

If  A is a 5 x 5 non zero matrix s.t  $XAX^{-1 }=A$ for all invertible matrices $X$, One of the eigen values of $A$ is $2$. Then what is the determinant of $A$?

 

Attempt: I think A should be $2 I .$ But I need some hint in proving this please.

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