# is matrix $A$ similar to matrix scalar $\times A$?

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 $$P$$?)

• Welcome to MSE. Did you mean to put $A^{-1}$ instead of $A$? What have you tried? Show us your thinking. – Ted Shifrin Jan 13 at 0:53