Transpose a 2D Matrix (C++), Discuss Memory/Cache Trade-offs

Given a 2D matrix A of size R x C, implement matrix transpose and return B of size C x R such that B[j][i] = A[i][j]. Requirements Provide the core transpose implementation (C++ or pseudocode). Discuss engineering considerations: Impact of row-major vs column-major on access patterns Cache friendliness (how to reduce cache misses) Performance bottlenecks for large matrices Whether to use blocking/tiling and how tile size affects performance Constraints 1 ≤ R, C ≤ 10^4 (matrix can be large; do not assume it fits in cache). Sample tests [[1,2,3],[4,5,6]] → [[1,4],[2,5],[3,6]] [[7]] → [[7]] [[1,2],[3,4]] → [[1,3],[2,4]] [[1,2,3]] → [[1],[2],[3]] [[1],[2],[3]] → [[1,2,3]] Example Input 2 3 1 2 3 4 5 6 Output 3 2 1 4 2 5 3 6