Verify cayley halimitton theorem and find A inverse 

The **Cayley-Hamilton theorem** states that every square matrix satisfies its own characteristic equation. To verify the Cayley-Hamilton theorem for a given matrix \( A \), we need to follow these steps:

1. **Find the characteristic polynomial** of \( A \).
2. **Substitute** the matrix \( A \) into its own characteristic equation.
3. **Verify** that the matrix satisfies the characteristic equation.

After verifying the Cayley-Hamilton theorem, we can use it to find the inverse of \( A \).

### Step 1: Find the characteristic polynomial of \( A \)

The characteristic polynomial of a matrix \( A \) is given by:
\[
p(\lambda) = \det(A - \lambda I)
\]
where \( I \) is the identity matrix of the same size as \( A \), and \( \lambda \) is the eigenvalue variable.

Let me know the matrix \( A \) you are working with, and I will proceed with the verification and find its inverse for you.

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Verify Cayley-Hamilton theorem and find A inverse

Learn how to verify the Cayley-Hamilton theorem for a matrix and use it to find the matrix inverse. This detailed step-by-step guide covers key linear algebra concepts, including the characteristic polynomial and matrix inverse. Suitable for undergraduate students.

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