If $g$ solves the Einstein equation, does $kg$ also solve the Einstein equation?

Question

Simple question. If $g_{ij}$ is a solution to:

$R_{ij}-\frac{1}{2} g_{ij}R+g_{ij} \Lambda = 0$,

i.e. the vacuum equation, will $kg_{ij}$ where $k$ is constant also solve it? I know that the Ricci tensor is scale invariant, so my initial answer would be "no"?