code: def backward(self, indexes, gy):
      (x,) = self.get_retained_inputs()
      (detx,) = self.get_retained_outputs()
      (gy,) = gy
      inv_x = chainer.functions.batch_inv(
          chainer.functions.transpose(x, (0, 2, 1))
      )
      gy = chainer.functions.broadcast_to(
          gy[:, None, None], inv_x.shape
      )
      detx = chainer.functions.broadcast_to(
          detx[:, None, None], inv_x.shape
      )
      grad = gy * detx * inv_x
      return (grad,)
  
file_path: chainer/chainer/functions/math/det.py
imports: import chainer
  from chainer import function_node
  import chainer.functions
  from chainer.utils import precision
  from chainer.utils import type_check
label_desc: Use image node_id 4 for calling the BatchDet obj's underlying member method code with example usage: obj.backward(indexes, gy) and returns: grad