Finding matrix and the inverse is given

[Vendor]

Homework Statement

Using the following information, find the matrix A

(I+2A)^-1 =

[-1 2]
[4 5]

Homework Equations

AA^-1 = I

The Attempt at a Solution

none. I have no idea how should I start. The inverse on the whole left side is driving me crazy.

 

[FactChecker]

Start reversing the operations of (I+2A)^-1 one by one till you strip it down to A. You know the matrix value of (I+2A)^-1

 

[Vendor]

Start reversing the operations of (I+2A)^-1 one by one till you strip it down to A. You know the matrix value of (I+2A)^-1

Thanks a lot for the response, so basically start getting the inverse of the given matrix and get rid of the -1 on the left then and keep going, is that what you mean ?

Sounds logical, not sure why I never thought of it that way. Again thank you.

 

[FactChecker]

That's right.

 

[Vendor]

Solved and understood. Thanks again :)