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Alg 2 BC U4
Day 2: 2x2 Matrices, Determinants and Inverses
A square matrix:
Every square matrix has a corresponding DETERMINANT, which has a value.
Finding the determinant for a 2x2 matrix:
Evaluate: a)
4 3
5
2
a b
a b 
If A  
, then det A 
 ad  bc

c
d
c
d


=
b)
5
2
10
4
=
Quick Review of Multiplicative Identities:
For any real number a, the multiplicative identity of a is __________ because __________________________.
Square matrices also have a multiplicative identity:
a b 
a b 
What matrix, when multiplied by 
yields

c d  ?
c d 


For an n x n square matrix, the multiplicative identity matrix is an n x n matrix
with ______ along the diagonal and _____ elsewhere.
Quick Review of Multiplicative Inverses:
For any real number a, the multiplicative inverse of a is ______ since __________________________.
Some, but not all, square matrices have multiplicative inverses!
If A and A 1 are multiplicative inverses, then A  A1  A1  A  the identity matrix.
1 0 0 
1 0 
1
1
, A  A  A  A  0 1 0  , etc.
A A  A  A  



0 1 
0 0 1 
1
1
Example: Show that B is the multiplicative inverse of A.
2 3
 2 3
, B
A


1 2
 1 2 
Finding the Inverse of a 2x2 Matrix:
a b 
Let A  
.
c d 
If det A  ____ , then A has an inverse and A1 
Find the inverse of the following matrices.
 2 2 
M= 

 5 4 
Using Inverses to Solve Equations:
If A and B are matrices, and A  X = B, then
Remember, multiplication is not commutative
so A-1 needs to be on the left side of B!
3 9
N= 

2 6
Solve for X:
 2 5
 2
1 3X  2


 