Explanation:

Finding the Eigen values of A²:

- Let's assume A is a square matrix with eigen values 2, 3, and 4.
- To find the eigen values of A², we need to find the eigen values of A².
- The eigen values of A² are the squares of the eigen values of A.
- Therefore, the eigen values of A² will be 2² = 4, 3² = 9, and 4² = 16.

Explanation in Detail:

- When we square a matrix A, we are essentially squaring each element in the matrix.
- The eigen values of the squared matrix A² are the square of the eigen values of the original matrix A.
- This property is derived from the definition of eigen values and eigen vectors.
- Eigen values represent the scaling factor by which an eigen vector is stretched when it is multiplied by the matrix.
- When we square a matrix, the eigen values are squared because the stretching factor is applied twice.
- Therefore, the eigen values of A² are the squares of the eigen values of A.

Conclusion:

- In conclusion, if the eigen values of a matrix A are 2, 3, and 4, then the eigen values of A² will be 4, 9, and 16.
- This relationship holds true for any square matrix and its square.