It's an issue of memory cache.
matrix[i][j] has better cache hits than matrix[j][i], since matrix[i][j] has more continuous memory accessing chances.
For example, when we access matrix[i][0], the cache may load a continuous segment of memory containing matrix[i][0], thus, accessing matrix[i][1], matrix[i][2], ..., will benefit from caching speed, since matrix[i][1], matrix[i][2], ... are near to matrix[i][0].
However, when we access matrix[j][0], it is far from matrix[j - 1][0] and may not been cached, and can not benefit from caching speed. Especially, a matrix is normally stored as a continuous big segment of memory, and the cacher may predicate the behavior of memory accessing and always cache the memory.
That's why matrix[i][j] is faster. This is typical in CPU cache based performance optimizing.
