In these lessons, we will learn about the identity matrix and inverse matrices.
We also feature a matrix calculator that will help you to find the inverse of a 3×3 matrix. Use it to check your answers.
A square matrix, I is an identity matrix if the product of I and any square
matrix A is A.
i.e. IA = AI = A
For a 2 × 2 matrix, the identity matrix for multiplication is
When we multiply a matrix with the identity matrix, the original matrix is unchanged.
If the product of two square matrices, P and Q, is the identity matrix
then Q is an inverse matrix of P and P is the inverse matrix of Q.
i.e. PQ = QP = I
The inverse matrix of A is denoted by A-1. (read as “A inverse”)
AA-1 = A-1A = I
Note that the inverse of A-1 is A.
Given that B is the inverse of A, find the values of x and y.
Since B is an inverse of A, we know that AB = I
1 – 2y = 1
2y = 0
y = 0
2x = 1
The Identity Matrix
This video introduces the identity matrix and illustrates the properties of the identity matrix.
A n × n square matrix with a main diagonal of 1’s and all other elements 0’s is called the identity matrix In.
If A is a m × n matrix, then ImA = A and AIn = A.
Is A is a n × n square matrix, then
AIn = InA = A.
Determining a 2×2 Inverse Matrix Using a Formula
This video explains the formula used to determine the inverse of a 2x2 matrix, if one exists.
Determine the inverse of matrix A.
How to find the inverse of a 2×2 matrix using the inverse formula?
Identity matrix and inverse matrix
This matrix calculator will help you find the inverse of a 3×3 matrix.
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