# Solution Alignment The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests. ## Problem Restatement For a 3x3 matrix, write Python code to: (a) transpose it in-place; (b) swap any two rows and any two columns; (c) reverse a specified column and reverse all rows; and (d) rotate the matrix 90 degrees clockwise. Include example inputs and resulting matrices for each operation. ## Recommended Approach Represent each cell as a state. Use BFS for minimum-distance propagation, DFS with memoization for longest monotonic paths, and careful boundary checks for simulation. Store obstacles or visited cells in sets when the grid is sparse. ## Correctness The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call. ## Complexity A full grid traversal is O(mn) time and O(mn) space in the worst case. Sparse simulation is O(number_of_commands) plus obstacle storage. ## Edge Cases and Tests Empty grid, one row/column, blocked start or target, boundaries, repeated visits, and tie-breaking among equal-distance cells.