input: 
  class Matrix: 
      def __init__(self, m, n, lst): 
          self.m = m             
          self.n = n             
          self.mat = [] 
    
          c = 0
          for i in range(self.m): 
              a =[] 
              for j in range(self.n): 
                      a.append(lst[c]) 
                      c += 1
              self.mat.append(a) 
    
      def __str__(self): 
          output = ""
          for i in self.mat: 
              for j in i: 
                  output += str(j) + " "
              output += '\n'
          return output 
    
      def add(self, mat2): 
          for i in range(self.m): 
              for j in range(self.n): 
                  self.mat[i][j] += mat2.mat[i][j] 
    
      def sub(self, mat2): 
          for i in range(self.m): 
              for j in range(self.n): 
                  self.mat[i][j] -= mat2.mat[i][j]
      
      def mul(self, mat2): 
          result = [] 
          for i in range(self.m): 
              a =[] 
              for j in range(mat2.n): 
                  s = 0
                  for k in range(self.n): 
                      s += self.mat[i][k] * mat2.mat[k][j] 
                  a.append(s) 
              result.append(a) 
          self.mat = result 
          self.m = len(result) 
          self.n = len(result[0]) 
    
      def transpose(self):
          result = [[self.mat[j][i] for j in range(len(self.mat))] for i in range(len(self.mat[0]))]
          self.mat = result 
          self.m = len(result) 
          self.n = len(result[0])
  
  # Example usage:
  mat1 = Matrix(2, 2, [1, 2, 3, 4])
  mat2 = Matrix(2, 2, [5, 6, 7, 8])
  mat1.add(mat2)
  print(mat1)
  # Output:
  # 6 8 
  # 10 12
  
  mat3 = Matrix(2, 2, [1, 2, 3, 4])
  mat3.transpose()
  print(mat3)
  # Output:
  # 1 3 
  # 2 4
  
output:     
      def scalar_mul(self, scalar): 
          for i in range(self.m): 
              for j in range(self.n): 
                  self.mat[i][j] *= scalar 
    
      def is_square(self): 
          return self.m == self.n 
    
      def is_symmetric(self): 
          if not self.is_square(): 
              return False 
          for i in range(self.m): 
              for j in range(self.n): 
                  if self.mat[i][j] != self.mat[j][i]: 
                      return False 
          return True 
    
      def trace(self): 
          if not self.is_square(): 
              return None 
          return sum(self.mat[i][i] for i in range(self.m)) 
    
      def __eq__(self, other): 
          if self.m != other.m or self.n != other.n: 
              return False 
          for i in range(self.m): 
              for j in range(self.n): 
                  if self.mat[i][j] != other.mat[i][j]: 
                      return False 
          return True 
    
      def __ne__(self, other): 
          return not self.__eq__(other)
  