Description
Given two sparse matrices A and B, return the result of AB.

You may assume that A’s column number is equal to B’s row number.

Example:

A = [
  [ 1, 0, 0],
  [-1, 0, 3]
]

B = [
  [ 7, 0, 0 ],
  [ 0, 0, 0 ],
  [ 0, 0, 1 ]
]


     |  1 0 0 |   | 7 0 0 |   |  7 0 0 |
AB = | -1 0 3 | x | 0 0 0 | = | -7 0 3 |
                  | 0 0 1 |

Auxiliary Table Solution

Code below is a standard way of solving this problem.
A better solution inspired by one of the CMU lectures is here

public class Solution {
    public int[][] multiply(int[][] A, int[][] B) {
        boolean[] rowCheck = new boolean[A.length];
        boolean[] colCheck = new boolean[B[0].length];
        checkRow(rowCheck, A);
        checkCol(colCheck, B);
        int[][] ret = new int[A.length][B[0].length];
        
        for (int i=0; i<A.length; i++) {
            if (rowCheck[i]==false) continue;
            for (int j=0; j<B[0].length; j++) {
                if (colCheck[j]==false) continue;
                for (int k=0; k<B.length; k++) {
                    ret[i][j] += A[i][k] * B[k][j];
                }
            }
        }
        return ret;  
    }
    
    private void checkRow(boolean[] rowCheck, int[][] A) {
        for (int i=0; i<A.length; i++) {
            for (int j=0; j<A[0].length; j++) {
                if (A[i][j] != 0) {
                    rowCheck[i] = true;
                    continue;
                }
            }
        }
    }
    
    private void checkCol(boolean[] colCheck, int[][] B) {
        for (int j=0; j<B[0].length; j++) {
            for (int i=0; i<B.length; i++) {
                if (B[i][j] != 0) {
                    colCheck[j] = true;
                    continue;
                }
            }
        }
    }
}

imgRuntime: 45-78ms