# A question in finding a invert of a certain operator

• transgalactic
In summary, the conversation is discussing the concept of matrix inverse and its properties. The participants are trying to understand how A-1 works and how it can be useful in solving certain operations. They also discuss the formula A2- A+ I= 0 and its relation to A-1. The conversation ends with a question about the value of A-1.
You are given that A2- A+ I= 0. Just basic algebra tells you that is the same as I= A- A2= A(I- A). Now, stop worrying about formulas, etc. and think about what A-1 means.

it means that if we take the image of a certain basis
and put it into the A^-1 we get the original basis

how its going to help me??

thought of certain solution of making some basic multiplication
operations

i got the resolt

A^-1=I-A
is it ok??

Last edited:
transgalactic said:
it means that if we take the image of a certain basis
and put it into the A^-1 we get the original basis
?? No, A-1 doesn't mean anything like that: it means the linear operation that "undoes" A. A-1Ax= x and AA-1x= x.

how its going to help me??

thought of certain solution of making some basic multiplication
operations

i got the resolt

A^-1=I-A
is it ok??
My point was that A(I- A)= I shows that I -A does exactly what we want of the inverse: AA-1= I. Since A(I-A)= I, (and inverses are unique), A-1= I- A.

what is the value of A^-1

## 1. What is an invert of an operator?

An invert of an operator is a mathematical function that reverses the effects of the original operator. It is denoted as the reciprocal of the original operator and is used to undo the operation performed by the original operator.

## 2. Why is finding the invert of an operator important?

Finding the invert of an operator is important because it allows us to solve equations involving the original operator. It also helps in simplifying complex mathematical problems and finding solutions to various scientific and engineering applications.

## 3. How do you find the invert of an operator?

The process of finding the invert of an operator varies depending on the type of operator. In general, it involves finding the inverse function of the original operator, which is done by manipulating the equation in terms of the inverse function. This process can be complex and may require advanced mathematical techniques.

## 4. What are some common examples of operators and their inverses?

Some common examples of operators and their inverses include addition and subtraction, multiplication and division, logarithms and exponentiation, and differentiation and integration. In each case, the inverse function undoes the operation performed by the original operator.

## 5. Are there any limitations to finding the invert of an operator?

Yes, there are limitations to finding the invert of an operator. In some cases, an operator may not have an inverse function, making it impossible to find its invert. Additionally, the process of finding the invert of an operator can be complex and may not always result in a simple solution.

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