Invertible Matrix Theorem - Expii

Adjoint and Inverse of a Matrix With Their Relation, Properties, Examples

4. (9 points) Give examples of A and B such that(a) A B is not invertible although A and B are invertible.(b) A B is invertible although A and B are not invertible(c) All of A, B and A B are invertible.(d) In the last case, show that B^-1 A^-1 is also invertible and find a formula for its inverse.(Hint: Check this out A^-1(A B)B^-1)

How to Determine if a Matrix is invertible | Precalculus | Study.com

Singular Matrix | Definition, Properties & Example