Matrix Multiplication Calculator

Welcome to the best online Matrix Multiplication Calculator. This tool, also known as the Multiplying Matrices Calculator, can multiply one matrix by another in three easy steps.

Step 1) Select your matrix sizes: Here you make the sizes of the two matrices that you want to multiply together. We call them Matrix-a and Matrix-b. You choose how many rows and columns each matrix should have (row × column).

a:  ×
b:  ×

Step 2) Fill in values for Matrix-a:

a11
a12
a13
a21
a22
a23

Step 3) Fill in values for Matrix-b:

b11
b12
b13
b14
b21
b22
b23
b24
b31
b32
b33
b34

That's it. When you have entered all the values, press "submit" below to see the answer.

Here is how the Matrix Multiplication Calculator works

First, we create the answer matrix (Matrix-c) using the number of rows from Matrix-a and the number of columns from Matrix-b.

Next, to calculate c11, we multiply each value in the first row in Matrix-a by each value in the first column of Matrix-b, and add them up. Then, to calculate c12, we multiply each value in the first row in Matrix-a by each value in the second column of Matrix-b and add them up, and so on like this:

c11 = (a11 × b11) + (a12 × b21) + ....

c12 = (a11 × b12) + (a12 × b22) + ....

etc..

Then, for the next row of Matrix-c, to calculate c21, we multiply each value in the second row in Matrix-a by each value in the first column of Matrix-b and add them up. Then, to calculate c22, we multiply each value in the second row in Matrix-a by each value in the second column of Matrix-b and add them up, and so on like this:

c21 = (a21 × b11) + (a22 × b21) + ....

c22 = (a21 × b12) + (a22 × b22) + ....

etc..

And then we repeat that for each row as needed. That's all there is to it folks!