Matrix Multiplication (Recursive) C++

Question

I am trying to write a program that will do matrix multiplication recursively using a 2D array represented as a 1D array in column major order. Here is what I have right now.

This is the main method for the recursive calls.

vector<double> recursive_mult(int n, vector<double> A, vector<double> B) {
    vector<double> C;
    if (n == 1) {
        C.push_back(A[0] * B[0]);
    } else {
        C = equals(C, recursive_mult(n/2, matrix_partitioner(n/2, 0, A), matrix_partitioner(n/2, 0, B)) 
                    + recursive_mult(n/2, matrix_partitioner(n/2, 1, A), matrix_partitioner(n/2, 2, B)));
        C = equals(C, recursive_mult(n/2, matrix_partitioner(n/2, 0, A), matrix_partitioner(n/2, 1, B)) 
                    + recursive_mult(n/2, matrix_partitioner(n/2, 1, A), matrix_partitioner(n/2, 3, B)));//1
        C = equals(C, recursive_mult(n/2, matrix_partitioner(n/2, 2, A), matrix_partitioner(n/2, 0, B)) 
                    + recursive_mult(n/2, matrix_partitioner(n/2, 3, A), matrix_partitioner(n/2, 2, B)));//2
        C = equals(C, recursive_mult(n/2, matrix_partitioner(n/2, 2, A), matrix_partitioner(n/2, 1, B)) 
                    + recursive_mult(n/2, matrix_partitioner(n/2, 3, A), matrix_partitioner(n/2, 3, B)));//3
    }
    return C;
}

Matrix partitioner gets a specific quadrant from the given matrix.

vector<double> matrix_partitioner(int n, int section, vector<double> A) {
    vector<double> C(n*n);
    int start_i, start_j, tmp_j;
    if (section == 0) {
        start_i = 0;
        tmp_j = 0;
    }
    else if (section == 1) {
        start_i = 0;
        tmp_j = n;
    }
    else if (section == 2) {
        start_i = n;
        tmp_j = 0;
    }
    else if (section == 3) {
        start_i = n;
        tmp_j = n;
    }
    for (int i = 0; i < n; i++) {
        start_j = tmp_j;
        for (int j = 0; j < n; j++) {
            C[i+(j*n)] = A[start_i+(start_j*(n*2))];
            start_j++;
        }
        start_i++;
    }
    return C;
}

Equals puts the result from adding the two matrices together into C

vector<double> equals(vector<double> A, vector<double> B) {
    for (int i = 0; i < B.size(); i++) {
        A.push_back(B[i]);
    }
    return A;
}

I have also overloaded the '+' operator to make adding the matrices easier.

These are the results I am getting (I have the iterative method results to compare to, they both use the same print method):

Iterative
| 250 260 270 280  |
| 618 644 670 696  |
| 986 1028 1070 1112  |
| 1354 1412 1470 1528  |
Recursive
| 250 270 986 1070  |
| 260 280 1028 1112  |
| 618 670 1354 1470  |
| 644 696 1412 1528  |

Clearly my recursive results are not correct (or at least not in the right order) but I do not know how to fix my code to make it print properly. Can someone help me fix this code?

I have tried re-ordering the equals statements, but no luck