Finding a matrix with the following property

Question

I have one $n \times n$ symmetric matrix $B$. Let $p$ be a scalar, I want to multiply the diagonal elements of $B$ by $p$. Let now $C$ denote the resultant matrix of the process described. Is there some matrix $A$, such that $AB = C$?

Answer 1

Assuming $B$ is nonsingular, $A = C B^{-1}$. Or did you want an $A$ that doesn't depend on $B$ and $C$? That won't exist.