ϵr={{ϵ,0,0},{0,ϵ,0},{0,0,ϵ}};
ϵc=ϵ*{{ρ,0,0},{0,1/ρ,0},{0,0,ρ}};
Λ={{a,0,0},{0,b,0},{0,0,c}};
ϵc2=Dot[Λ,ϵc]
Acr={{Cos[θ],-ρ*Sin[θ],0},{Sin[θ],ρ*Cos[θ],0},{0,0,1}};
Acrt=Transpose[Acr];
detAcr=ρ;
ϵr2=Simplify[Dot[Dot[Acr,ϵc2],Acrt]/detAcr]//MatrixForm