def matmul(quaternion1: type_alias.TensorLike,
             quaternion2: type_alias.TensorLike,
             name: str = "quaternion_matmul"
             ) -> tf.Tensor:
  """Multiplies matrices of quaternions.
  Note:
    In the following, A1 to An are optional batch dimensions.
  Args:
    quaternion1:  A tensor of shape `[A1, ..., An, M1, M2, 4]`, where M1 and M2 are the matrix dimensions, and the last dimension
      represents a quaternion.
    quaternion2:  A tensor of shape `[A1, ..., An, M2, M3, 4]`, where M2 and M3 are the matrix dimensions, and the last dimension
      represents a quaternion.
    name: A name for this op that defaults to "quaternion_matmul".
  Returns:
    A tensor of shape `[A1, ..., An, M1, M3, 4]` representing matrices of quaternions.
  Raises:
    ValueError: If the shape of `quaternion1` or `quaternion2` is not supported.
  """