Section 4.4: Identity and Inverse 

Because the multiplication identity is equal to 1, 
each square matrix has it's own identity form. 
For a 2 by 2


For a 3 by 3 


Two 2 by 2 matrices are inverses of each other if their products 
(in both orders) equal the identity matrix. 
Two 3 by 3 matrices are inverses of each other if their products 
(in both orders) equal the identity matrix. 

The inverse of a 2 by 2 matrix is found by switching the 
a and d numbers and making opposite the b and c numbers. 
(by placing a negative sign in front of the b and c spots, 
you would make positive numbers negative and negative numbers positive.) 


The inverse of a 3 by 3 matrix Because the inverse of a 3 by 3 matrix 
is virtually insane to compute, use your T1-83 calculator to simply plug 
in the numbers and then call up the inverse. You can prove that your inverse 
is really an inverse by multiplying the first matrix by the inverse, and if it 
yields the identity matrix, then it is the inverse! If the determinant of a 
matrix equals 0, then it does not have an inverse. 

You try: 
1) Find the inverse of the matrix: 


2) Decided whether the matrix has an inverse: 





Answers: 

1) 


2) No it does      
      not.