 ## Tutoring on Determining Inverse Matrices

Learning Objectives:

#### Understand Inverse Matrices.

Math Tutoring on Determining Inverse Matrices

An (n x n) square matrix with a main diagonal consist of 1's and all other elements are 0's is called the Identity Matrix In

If A is an (m x n) matrix, then ImA = A and AIn = A

If A is an (n x n) square matrix, then AIn = InA = A.

Now if A is an (n x n) invertible matrix such that AB = BA = In, then B is the inverse of A and is denoted by A-1.

We need to remember that, not all matrices have an inverse

We can determine Inverse Matrices during math tutoring in two steps:

1) Create an augmented matrix in the form [A|In]

2) Perform row matrix operations resulting in an augmented matrix in the form [In|A-1].

The main idea here is to convert A into In on the left side of the augmented matrix. The right side will become A-1.

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Hook questions:

1.    What is the role of Identity Matrix in finding Inverse Matrix?

2.    What is Augmented Matrix?

3.    Define Invertible Matrix.

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