INVERSE MATRICESWill Lombard, Meg Kelly, Sarah Bazir

Inverse Matrices-the matrix which when multiplied by the

original matrix gives the identity matrix as the solution.

-the identity matrix for multiplication is a square matrix with a 1 for every element of the principal diagonal (top left to bottom right) and a 0 in all other positions.

the inverse of the matrix A = a b

c d

A-1=1 |A|

d -b

-c a= 1

ad-cb

d -b

-c a

Inverse Matrices; Step by StepYour matrix will be established in a particular dimension, for

this particular example, we will use a 2 by 2 matrix which is nonsingular. (nonsingular refers to the fact that it does indeed have an inverse, not all matrices have inverses.)

1. Reverse the positions of the top left and bottom right digits in the matrix.

2. Switch the operations of the digits located in the top right and bottom left positions.

3. Your result will be the inverse of the original matrix.

Example of an Inverse Matrix Problem

-4 3

-3 2

= A Determinant of A= (-4 * 2) - (3 * -3)Determinant of A= -8 - (-9)Determinant of A= 1

Rearranged matrix A =2 3

-3 -4

1. 2.

3.

(1/Determinant of A) * Rearranged Matrix A = Inverse4.

(1/1) * 2 3

-3 -4

2 3

-3 -4=