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Even you let $\phi=A$, the statement still not hold in general.
Let $a=(1,1)$$s=(1,1)$, $\phi=A=(1,-1)$, $M=diag(2,1)$.
Let $a=(1,1)$, $\phi=A=(1,-1)$, $M=diag(2,1)$.
Let $s=(1,1)$, $\phi=A=(1,-1)$, $M=diag(2,1)$.