In these lessons, we will learn about the identity matrix and inverse matrices.
We also have a matrix calculator that will help you to find the inverse of a 3x3 matrix. Use it to check your answers.
More Lessons on Matrices
A square matrix, I
is an identity matrix
if the product of I
and any square matrix A
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 following video explains more about identity matrix and inverse matrix.
The Identity Matrix
This video introduces the identity matrix and illustrates the properties of the identity matrix.
Determining a 2x2 Inverse Matrix Using a Formula
This video explains the formula used to determine the inverse of a 2x2 matrix, if one exists.
This video explains how to find the inverse of a 2x2 matrix using the inverse formula.
This matrix calculator will help you find the inverse of a 3x3 matrix.
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