Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Matrix "Division"

Name: Muhammad S. 
Status: student        
Grade: 9-12 
Country: Pakistan
Date: Fall 2012

Matrices can be added, subtracted, and multiplied. Why is division not allowed?

It is, in a manner. Some square matrices can be inverted, so that the inverse matrix acts in many ways as a reciprocal.

Richard E. Barrans Jr., Ph.D., M.Ed. Department of Physics and Astronomy University of Wyoming

Hi Muhammad,

You CAN divide matrices. But only certain matrices apply and the rules of operation are slightly different.

Firstly, matrices are not real numbers. It is a system of equations that represent vectors and polynomial equations.

Secondly, division of real numbers is based on multiplication where a * b is rewritten as a * (1/b) where (1/b) is called the inverse of b. With the restriction that b <> 0. In parallelism, dividing two matrices A/B is again A * Inverse B. But the inverse of B implies that B is a square matrice AND its determinant is non zero. Sound familiar?

So in summary, you can divide matrices using multiplication, but the dividing matrice must be invertible, a square matrix and its determinant must not equal zero.

-Alex Viray

Muhammad, With matrices, division is not definite. There are usually many different possible results to a division problem with matrices. A simple example is (4) divided by (1 1 1 1). I cannot type well in multiple dimensions, so please accept the last matrix as a column. Three possible answers are (4 0 0 0), (1 1 1 1), and (2 0 2 0). Addition, subtraction, and multiplication have definite answers.

Dr. Ken Mellendorf Physics Instructor Illinois Central College

Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 223
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: November 2011
Weclome To Newton

Argonne National Laboratory