procedure multiply_matrix (m1, m2)
  result := [] # to hold the final matrix
  every row1 := !m1 do { # loop through each row in the first matrix
    row := []
    every colIndex := 1 to *m1 do { # and each column index of the result
      value := 0
      every rowIndex := 1 to *m2 do {
        value +:= row1[rowIndex] * m2[rowIndex][colIndex]
      }
      put (row, value)
    }
    put (result, row) # add each row as it is complete
  }
  return result
end