Recall that a Monge array satisfies the property that for all i < j and k < l, M[i][k] + M[j][l] ≤ M[i][l] + M[j][k]. Use this property to optimize matrix operations.

For matrix multiplication on a Monge array, observe that the resulting matrix may not retain the Monge property. Identify which operations preserve or violate this property.

To compute the minimum path sum in a Monge array, leverage the property to reduce the problem to O(n) time using dynamic programming with a deque for monotonic queue optimization.