❖ In this video, we have explained how to find the inverse of a 2x2 matrix, which is a precalculus video tutorial.

❖ To find the inverse of a 2x2 matrix, we have mentioned two ways to answer.

❖ The first way to answer (The first method):
You need to write an augmented matrix containing the original matrix and the identity matrix (which has the same size as the original matrix),

Then,
You need to convert the original matrix into the identity matrix using elementary row operations
(Apply Reduced Row Echelon Form (RREF) for the left side of the augmented matrix).

The identity matrix will convert into the inverse of the original matrix as long as you apply the same elementary row operations for the augmented matrix.

❖ The second way to answer (The second method):
You need to do a simple formula to find the inverse of a matrix.

❖ Finally, you can confirm or check to see if you have the right answer by
multiplying (the matrix) by (its inverse) and you have to get (the identity matrix).

❖ (The matrix A) multiplied by (the inverse of the matrix A) equal to (the identity matrix) of the same size as A,

so, if A inverse exists then

A * A^(-1) = Identity matrix.

❖ Also, we have explained in this video that if the inverse of the matrix does not exist (DNE).

Note:
If A is not a Square Matrix, then the inverse of matrix A is DNE.

The Square Matrix is a matrix with
the number of rows = the number of columns.

❖ The number of rows and columns that a matrix has is called its size, order, or dimension.

0:00 ❖ Introduction
0:32 Definition
2:25 How to find the inverse of a matrix?
10:59 The important note
12:08 Solve 1 (The first method)
16:42 Solve 1 (The second method)
25:40 To confirm or check our answer for 1
29:24 Solve 2 (The first method)
31:12 Solve 2 (The second method)

The link to this playlist (Linear Algebra):
   • Linear Algebra  

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