# Inverses of 3 by 3 Matrices

This applet is a calculator for finding inverses of 3 by 3 matrices, by calculating cofactors and determinants. The method is displayed fully, including cases of singular matrices which have no inverse. You can enter any matrix with integer elements up to 100.

###### Author and programmer: Ron Barrow

UK Years 12-13, KS5, OCR FP1, Edexcel FP3, AQA FP4, GCE Further Mathematics, Algebra and Functions

US - Grades 11, 12 - Algebra II

Instructions below See also: 2D matrix transformations AQA Further Pure 4 textbook (from AQA site)

## How to Use this Applet

This applet is designed as a calculator for inverses of 3 by 3 matrices, but also displays the method of calculation, which in this case uses cofactors. You can click-and-drag the numbers in matrix A (top left) to change their values. You can also press "reset" to change to the 3 by 3 indentity matrix, or press "random" to generate a random new matrix. All the calculations are then done automatically. Clicking the numbers in matrix B, the matrix of cofactors of A, will demonstrate how each cofactor is calculated from matrix A. Try it for yourself and see. You can treat this applet as simply a calculator, or you can see some of the beauty of matrices and how they behave. You can get some real insight just by looking. Enjoy!