Suppose we have a 2×2 matrix A, which has 2 rows and 2 columns:
| A = |
|
Suppose we also have a 2×2 matrix B, which has 2 rows and 2 columns:
| B = |
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To multiply matrix A by matrix B, we use the following formula:
| A x B = |
|
This results in a 2×2 matrix.
The following examples illustrate how to multiply a 2×2 matrix with a 2×2 matrix using real numbers.
Example 1
Suppose we have a 2×2 matrix C, which has 2 rows and 2 columns:
| C = |
|
Suppose we also have a 2×2 matrix D, which has 2 rows and 2 columns:
| D = |
|
Here is how to multiply matrix C by matrix D:
| C x D = |
|
This results in the following 2×2 matrix:
| C x D = |
|
Example 2
Suppose we have a 2×2 matrix E, which has 2 rows and 2 columns:
| E = |
|
Suppose we also have a 2×2 matrix F, which has 2 rows and 2 columns:
| F = |
|
Here is how to multiply matrix E by matrix F:
| E x F = |
|
This results in the following 2×2 matrix:
| E x F = |
|
Example 3
Suppose we have a 2×2 matrix G, which has 2 rows and 2 columns:
| G = |
|
Suppose we also have a 2×2 matrix H, which has 2 rows and 2 columns:
| H = |
|
Here is how to multiply matrix G by matrix H:
| G x H = |
|
This results in the following 2×2 matrix:
| G x H = |
|
Example 4
Suppose we have a 2×2 matrix I, which has 2 rows and 2 columns:
| I = |
|
Suppose we also have a 2×2 matrix J, which has 2 rows and 2 columns:
| J = |
|
Here is how to multiply matrix I by matrix J:
| I x J = |
|
This results in the following 2×2 matrix:
| I x J = |
|
Matrix Calculator
The examples above illustrated how to multiply 2×2 matrices by hand. A good way to double check your work if you’re multiplying matrices by hand is to confirm your answers with a matrix calculator. While there are many matrix calculators online, the simplest one to use that I have come across is this one by Math is Fun.