# Answer to Question #24749 in Linear Algebra for Shane

Question #24749

Ok so I have 3 matrix' and its A B C and I have to solve (-1 means inverse) for (A-1xB)-1xC so does (A inverse times B) the whole thing inverse times C = (B-1A)C?

Expert's answer

We know that (AB)^(-1) =B^(-1) * A^(-1).

Also, (A^(-1))^(-1)=A.

Now, we can simplify given expression as (A^(-1) * B)^ (-1) * C = (B^(-1) * A)*

C = B^(-1)AC, and this is a result.

Also, (A^(-1))^(-1)=A.

Now, we can simplify given expression as (A^(-1) * B)^ (-1) * C = (B^(-1) * A)*

C = B^(-1)AC, and this is a result.

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