Why an homogeneous inequality can be rewritten as another one?

Question

Consider the following homogeneous inequality

$$ A^{T}*P+PA\lt0, P > 0$$

where $A$ is a square given matrix. Since the inequality above is homogeneous, it can be rewriten as

$$A^{T}*P+PA<-I, P \geq I$$

Why is this possible?

Thanks