# Compute Prefix Matrix Products Given an ordered sequence of square integer matrices with the same dimensions, return every left-to-right prefix product. The first result is the first matrix, and each later result multiplies the preceding prefix product by the next input matrix. ### Function Signature ```text prefix_matrix_products(matrices: list[list[list[int]]]) -> list[list[list[int]]] ``` ### Valid Input Domain The input may be empty. Otherwise every matrix is a nonempty d by d integer matrix with the same d. Valid inputs are guaranteed to keep every intermediate and final entry within signed 64-bit range. ### Exact Output Semantics Return an empty list for empty input. For matrices A0 through An-1, output P0 through Pn-1 in order, where P0 = A0 and Pi = Pi-1 multiplied by Ai using standard row-by-column matrix multiplication. Matrix and row ordering are preserved exactly. ### Constraints - 0 <= matrices.length <= 100. - 1 <= d <= 20. - -1,000 <= matrix entry <= 1,000. - All intermediate results fit in signed 64-bit integers. ### Public Examples #### Example 1 Input: matrices = [[[1, 2], [0, 1]], [[2, 0], [1, 3]]] Output: [[[1, 2], [0, 1]], [[4, 6], [1, 3]]] The second prefix is the first matrix multiplied on the right by the second. #### Example 2 Input: matrices = [[[2]], [[-3]], [[4]]] Output: [[[2]], [[-6]], [[-24]]] For one-by-one matrices, prefix products reduce to cumulative scalar multiplication. ### Hints - Matrix multiplication order matters; do not reverse the new matrix and the accumulated prefix. - Each output must be a distinct matrix value even if internal buffers are reused.