Answer to Question #134046 in Linear Algebra for Senzo

Question

Let X ∈ Mn×n
, with det X = 0 (i.e. X is not invertible).
Prove or disprove:
There exists an  > 0 such that:
Y ∈ Mn×n, kX XY k <  =⇒ det Y = 0

Answer 1

$X\in Mn×n$ then $det X=0$.

So, if we take $Y=kX$, we get that $Y\in Mn×n$. And $det Y=0$. Q.E.D.