There was a witness to the crash, who investigators were speaking with today, but Mr Richards said it was not known if it was the instructor.
He said the plane was a Fletcher 24 Turbine Engine kerosene, which was the kind often used in agricultural applications.
CAA inspectors were at the site today combing through the wreckage to try to find the cause of the crash, he said.
"They'll be looking for mechanical or equipment failure or ... any major part of the aircraft that might have dislodged."
The inspectors were taking video footage and digital images to analyse, he said.
"They also need to determine whether they need to take the wreckage away from the site, and if they do it will mean they need to examine it more closely in controlled conditions."
Mr Richards said it was still early days with the inquiry, but the CAA wanted to find out if there were any "key learnings" for the industry about mechanical or equipment failure or pilot error.
He said there might also be tips to pass on to instructors on how to teach their students.
"We're not there to apportion blame to anybody."