This question is related to On a positivity of a matrix with trace entries.

Let $A_1, \cdots, A_m$ be strictly contractive $n\times n$ complex matrices .Is it true that $$\left(\begin{array}{cccc}Tr\{(I-A_1^*A_1)^{-1}\}&Tr\{(I-A_1^*A_2)^{-1}\}&\cdots &Tr\{(I-A_1^*A_m)^{-1}\}\\Tr\{(I-A_2^*A_1)^{-1}\}&Tr\{(I-A_2^*A_2)^{-1}\}&\cdots &Tr\{(I-A_2^*A_m)^{-1}\}\\ \cdots&\cdots&\cdots&\cdots\\Tr\{(I-A_m^*A_1)^{-1}\}&Tr\{(I-A_m^*A_2)^{-1}\}&\cdots &Tr\{(I-A_m^*A_m)^{-1}\} \end{array}\right)$$ is positive semidefinite.