Identity matrix

Identity matrix

In this lesson, we will learn about identity matrices. Identity matrices is an n by n matrix which all entries diagonal from the top left to the bottom right are 1's, and the rest of the entries are 0. There are many types of identity matrices, as listed in the notes section. We will learn how to apply matrix operations with these such as adding, subtracting, and multiplying. Lastly, we will see that identities have a special property. If two matrices are multiplicative inverses, then multiplying them would give an identity matrix.

Lessons

An identity matrix is an nn by nn matrix (written as InI_n) where all the entries that is diagonal from the top left to the bottom right are all 1’s, and the rest of the entries are 0. For example,

identity matrix of various n

are all identity matrices.
  • 1.
    a)
    The Identity Matrix

    b)
    Multiplicative Inverses


  • 2.
    Matrix Operation with the Identity Matrix
    You are given that Identity matrix and Matrix operation with identity matrix. Perform the following matrix operations:
    a)
    I3A I_3 \cdot A

    b)
    2A+4I32A+4I_3

    c)
    4B+2I2-4B+2I_2

    d)
    I2B I_2 \cdot B

    e)
    0I4 0 \cdot I_4


  • 3.
    Multiplicative Inverses
    Are the following matrices multiplicative inverses of each other?
    a)

    Identity matrix

    b)

    Identity matrix

    c)

    Identity matrix

    d)

    Identity matrix