code: def check(nu, location_matrix, scale_matrix_1, scale_matrix_2):
      if not isinstance(scale_matrix_1, MatrixSymbol):
          _value_check(
              scale_matrix_1.is_positive_definite != False,
              "The shape " "matrix must be positive definite.",
          )
      if not isinstance(scale_matrix_2, MatrixSymbol):
          _value_check(
              scale_matrix_2.is_positive_definite != False,
              "The shape " "matrix must be positive definite.",
          )
      _value_check(
          scale_matrix_1.is_square != False,
          "Scale matrix 1 should be " "be square matrix",
      )
      _value_check(
          scale_matrix_2.is_square != False,
          "Scale matrix 2 should be " "be square matrix",
      )
      n = location_matrix.shape[0]
      p = location_matrix.shape[1]
      _value_check(
          scale_matrix_1.shape[0] == p,
          "Scale matrix 1 should be"
          " of shape %s x %s" % (str(p), str(p)),
      )
      _value_check(
          scale_matrix_2.shape[0] == n,
          "Scale matrix 2 should be"
          " of shape %s x %s" % (str(n), str(n)),
      )
      _value_check(
          nu.is_positive != False, "Degrees of freedom must be positive"
      )
  
imports: from math import prod
  from sympy.core.basic import Basic
  from sympy.core.numbers import pi
  from sympy.core.singleton import S
  from sympy.functions.elementary.exponential import exp
  from sympy.functions.special.gamma_functions import multigamma
  from sympy.core.sympify import sympify, _sympify
  from sympy.matrices import ImmutableMatrix, Inverse, Trace, Determinant, MatrixSymbol, MatrixBase, Transpose, MatrixSet, matrix2numpy
  from sympy.stats.rv import _value_check, RandomMatrixSymbol, NamedArgsMixin, PSpace, _symbol_converter, MatrixDomain, Distribution
  from sympy.external import import_module
label_desc: Use image node_id 1 for calling the MatrixStudentTDistribution obj's underlying member method code with example usage: obj.check(nu, location_matrix, scale_matrix_1, scale_matrix_2) without return types