Implement matrix transforms and discuss eigenvalues

You are given a square matrix `A` (size `n × n`). 1. **Diagonal symmetry (transpose):** Transform `A` into its transpose (mirror across the main diagonal). Prefer an **in-place** algorithm when possible. 2. **Rotate 90 degrees:** Rotate the matrix by **90° clockwise** (again, ideally in-place). 3. **Eigenvalues:** Explain how you would compute the **eigenvalues** of `A`. ### Follow-ups - If `A` is a **sparse** matrix (most entries are zero), how would your representation and approach change for the above operations (especially eigenvalue computation)? - If the data is **3D** (a tensor / 3D array), how do “transpose/diagonal symmetry” and “rotation” generalize, and what does an eigenvalue-like concept become? Assume typical interview constraints such as `n` up to a few thousand for dense operations (memory permitting), and much larger for sparse matrices.