Prove the following: 1- if det(A)=0 , then AB is singular . ...

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Prove the following:

1- if det(A)=0 , then AB is singular . 

2- if A and B are invertible then AB is invertible . with (AB)^-1 = B^-1 A^-1

3- if A is invertible and B , C are inverses of A , the B=C . 

4- if A is invertible then det (A^-1)= 1/det (A) .

    • 5 years ago
    Since A is invertible, A is non-singular, that is |A| ≠ 0 ...
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