code: def flip_determinant(matrix, det):
      """Change sign of the determinant if it is negative.
  
      For a batch of matrices, multiply the matrices which have negative
      determinant by a diagonal matrix :math:`diag(1,...,1,-1) from the right.
      This changes the sign of the last column of the matrix.
  
      Parameters
      ----------
      matrix : array-like, shape=[...,n ,m]
          Matrix to transform.
  
      det : array-like, shape=[...]
          Determinant of matrix, or any other scalar to use as threshold to
          determine whether to change the sign of the last column of matrix.
  
      Returns
      -------
      matrix_flipped : array-like, shape=[..., n, m]
          Matrix with the sign of last column changed if det < 0.
      """
      if gs.any(det < 0):
          ones = gs.ones(matrix.shape[-1])
          reflection_vec = gs.concatenate(
              [ones[:-1], gs.array([-1.0])], axis=0
          )
          mask = gs.cast(det < 0, matrix.dtype)
          sign = (
              mask[..., None] * reflection_vec
              + (1.0 - mask)[..., None] * ones
          )
          return gs.einsum("...ij,...j->...ij", matrix, sign)
      return matrix
  
imports: import math
  import geomstats.backend
label_desc: Use image node_id 3 for calling a global function with example usage: flip_determinant(matrix, det) and returns: matrix, gs