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Is matrix $A$ similar to the matrix $\alpha A$, for a given scalar $\alpha$?

(Is there a $P$ such that $\alpha A=P^{-1}A^{-1}P$? And how can I find this $P$?)

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  • $\begingroup$ Welcome to MSE. Did you mean to put $A^{-1}$ instead of $A$? What have you tried? Show us your thinking. $\endgroup$ – Ted Shifrin Jan 13 at 0:53
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One approach [of many]: similar matrices have the same determinant.

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