We know that $(A⊗B)^{−1}=A^{−1}⊗B^{−1}$ for kronecker product
Is this true for Tracy–Singh product or Khatri–Rao product which is a kronecker product of partitioned matrices. See wiki kronecker product,
https://en.wikipedia.org/wiki/Kronecker_product#Tracy.E2.80.93Singh_product
That is: is $(A∘B)^{−1}=A^{−1}∘B^{−1}$ true where ∘ denotes Tracy-Singh product.