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!