Let $A$ be an algebra of finite global dimension. The Euler form on $A$ for an indecomposable module $M$ is defined as $\psi(M)=\sum\limits_{k=0}^{\infty}{(-1)^k dim( \operatorname{Ext}_A^k(M,M)) }$. Call $M$ Euler trivial in case $\psi(M)=dim (End_A(M,M))$.
Question: Do we have $\operatorname{Ext}_A^i(M,M)=0$ for all $i>0$ and indecomposable modules $M$ if and only if each indecomposable module $M$ is Euler trivial?
