Proof Verification for M matrices

Question

A matrix having non-negative diagonal entries and non-positive off-diagonal entries is called an M matrix. Its inverse is always non-negative. Suppose we have two positive constants $a_1$ and $a_2$ and $a_1<a_2$. Suppose the M matrix be $I-\alpha P$, where $I$ is the identity matrix and $P$ is component-wise non-negative and row sum is $1$, and $\alpha\in(0,1)$. I want to know if there is any possible way that $a_1 (I-\alpha P)$ and $a_2 (I-\alpha P)$ can be compared?
Is it correct to say: $(a_1(I-\alpha P))^{-1}\leq (a_2(I-\alpha P))^{-1}$.
This holds as $(I-\alpha P)^{-1}$ is non-negative and $\frac{1}{a_1}>\frac{1}{a_2}$. But without inverse it does not hold true.
Any further suggestions or counter-example to this will be really helpful