Identity and Inverse Matrices

Key Topics• Identity matrix: a square matrix,

multiplied with another matrix doesn’t change the other matrix (just like 1 is the multiplicative identity of real numbers)

Identity Matrix in Action

31

42

10

01

10

01

31

42

31401120

30141021

31

42

13010311

14020412

31

42

Notice: These two matrices are the same. Multiplying by the

identity matrix changed nothing

Notice: These two matrices are the same. Multiplying by the

identity matrix changed nothing

Key Topics• You might be wondering: why do I tell you

about the identity matrix ?? If it doesn’t do anything, why do we need to know what it is ??

• Inverses: two nXn matrices are inverses of each other if their product is the identity matrix

Checking for Inverse Matrices

• Determine whether the following pairs of matrices are inverses of one another:

Finding 2X2 Inverse Matrices

• To find the inverse of a 2X2 matrix, use the following method:

Basically this tells us to calculate the determinant, then multiply it’s inverse by

the rearranged matrix having a and d switch places and b and c as the opposite values

Inverse of Determinant Rearranged matrix

A-1 is the notation used to represent the

inverse of matrix A

If determinant is 0 there is no inverse!!

Practice• Find the inverse matrix for the following

matrices:

N/A