Question

Suppose that A, B, and C are invertible matrices of the same

size,Show that the product ABC is invertible and that
(ABC)-1= C-1B-1A-1.

Answer 1

Explanation:

Given that t A, B, and C are invertible matrices of the same

size.

To pr that
`(ABC)^(-1) = C^(-1)B^(-1)A^(-1).`

to pr that
`( ABC) (C^(-1)B^(-1)A^(-1))=e`

LS=
`( AB(C (C^(-1))B^(-1)A^(-1))\\=ABIB^(-1)A^(-1))\\=A(BB^(-1))A^(-1))\\=AA^(-1))\\=I`

Thus proved