We present an online matrix multiplication calculator. You can multiply matrices of size 2×2, 3×2, 4×4, 3×3, etc.
The multiplication process is performed from left to right, where A is multiplied by B. Follow these steps:
Choose the number of rows and columns for Matrix A.
Choose the number of rows and columns for Matrix B.
Click the “Create” button to generate the two matrices.
Fill in the required values and leave the values you want to remain 0.
Click the “A×B” button to multiply the matrices and display the result.
You can adjust the number of rows and columns by clicking on the matrix with the mouse and pressing the “+” button to add a row or column, and the “-” button to delete a row or column.
Note: We apologize for the limitation of 5×5 as the maximum number of rows and columns due to site load. We work for free to keep Wiki-Arabic ad-free. Help us to continue
First, as we know, the condition for matrix multiplication is that the number of columns of the first matrix must equal the number of rows of the second matrix. Therefore, if you encounter the following message while working on the calculator, you must focus and pay attention to the number of rows and columns of the matrices you have created.
2×2 Matrix Multiplication
Let’s have Matrix A2×2 and Matrix B2×2, each consisting of two rows and two columns. We note that the matrix condition is met because the number of columns of the first matrix (A) is equal to the number of rows of the second matrix (B). The multiplication process is performed as follows:
Multiply the first row of A by the first column of B (element-by-element and sum the results). Then, place the result in row 1, column 1 of the resulting matrix. 5⋅3+8⋅7 = 71
Multiply the first row of A by the second column of B (element-by-element and sum the results). Then, place the result in row 1, column 2 of the resulting matrix. 5⋅5+8⋅2 =30
Multiply the second row of A by the first column of B (element-by-element and sum the results). Then, place the result in row 2, column 1 of the resulting matrix. 3⋅3+3⋅7 =41
Multiply the second row of A by the second column of B (element-by-element and sum the results). Then, place the result in row 2, column 2 of the resulting matrix. 3⋅7+4⋅6 =21
A =
5
8
3
3
B =
3
5
7
2
2×3 Matrix Multiplication
Multiplying 2×3 matrices is easy, where the first matrix has 2 rows and 3 columns, and the second matrix has 3 rows to satisfy the condition for matrix multiplication. The number of columns of the second matrix does not matter, regardless of the number. Example:
C =
3
4
5
6
8
3
D =
1
4
2
8
0
6
The resulting matrix consists of two rows and two columns, a square matrix.
4×4 Matrix Multiplication
Care must be taken when multiplying 4×4 matrices, as both matrices consist of 4 rows and 4 columns, so there are many multiplication and addition operations. The resulting matrix also consists of 4 rows and 4 columns, which is a square matrix. An example of 4×4 matrix multiplication:
The details of the multiplication process are daunting, but with training and organization, they can be solved with ease. We performed 4x4x4 = 64 multiplication operations and 3x4x4 = 48 addition operations\! And of course, we multiplied each row of the first by all the columns of the second.
3×3 Matrix Multiplication
The following example illustrates 3×3 matrix multiplication, i.e., 3 rows and 3 columns. Of course, the resulting matrix is a 3×3 square matrix.
The multiplication operations in order:
9·0+√2·3+2·1
9·4+√2·7+2·2
9·9+√2√2+2·0.2
6·0+4·3+1·1
6·4+4·7+1·2
6·9+4√2+1·0.2
9·0+7·3+6·1
9·4+7·7+6·2
9·9+7√2+6·0.2
9·0+√2·3+2·1
9·4+√2·7+2·2
9·9+√2√2+2·0.2
6·0+4·3+1·1
6·4+4·7+1·2
6·9+4√2+1·0.2
9·0+7·3+6·1
9·4+7·7+6·2
9·9+7√2+6·0.2
2×1 Matrix Multiplication
For 2×1 matrix multiplication, the first matrix consists of two rows and one column, so the second matrix must consist of only one row and a number of columns. Let’s take the following example:
C =
1
2
M =
1
2
CM =
1×1
1×2
2×1
2×2
=
1
2
2
4
3×1 Matrix Multiplication
For 3×1 matrix multiplication, the first matrix has 3 rows and one column. Therefore, the second matrix must have a single row. Let’s take the example:
