matrix inverse rules

A-¹ is invertible, and (A-¹)-¹ =

A

AB is invertible and (AB)-¹ =

B-¹A-¹

The transpose is invertible and (A’)-¹ =

(A-¹)’

k(A)-¹

k-¹A-¹

if A is invertible and symmetric, what is A-¹

also symmetric

if A B C are all invertible nxm matrices, then (ABC)-¹ =

C−¹ (AB)-¹ = C-¹(B−¹A−¹) = C−¹B−¹A−¹