What is an identity?
In math the identity is the number you multiply by to have equivalent numbers.
For multiplication it is one.
5 * 1 = 5, of course. How is this useful?
3
If you need to have a denominator of 40 in the fraction
8
3

8
5
5

15
40

What is an inverse?
The inverse is a number when multiplied by another number equals one.
4

1
4

4

1
1
4

4
4

1
4

9
9 4

36
36

1

The identity matrix is a square matrix with one down the diagonals
In a 2 X 2 In a 3 X 3

1


0
0
1 

 

1



0
0
0
1
0
0


0
1




Find the matrices that when multiply together are the identity matrix.
How do we find the inverse?

?


?
?

?







2
1
8

3 



1


0
0

1 


Find the inverse
Find the determinant of


2

1 3
8


6 – ( - 8) = 14
We will flip the diagonal of top left and bottom right, then change the signs the bottom left to top right diagonal.



2
1
8
3





3
1

2
8



Putting the part together
Take the determinant and put it under one and multiply it by the moved matrix.
1
14


3
1

2
8



Lets see if it works
1
14


3
1

2
8






2
1
8
3


1
14


6
2

8

2
24
8


24
6



1
14


14
0
0
14





1
0
0
1



Can there be matrices without inverses?
Yes, when the determinate equals zero.




4
2
6
3



(

12

(

12 ))

0
Since a fraction can not have zero for a denominator. There would be no inverse.

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