An Easy Guide to Matrix Multiplication in Excel

This tutorial explains how to perform matrix multiplication in Excel.

Matrix Multiplication in Excel

To perform matrix multiplication in Excel, we only need to use one function: MMULT. This function returns the matrix product of two arrays and uses the following syntax:

MMULT(array1, array2)

where array1 and array2 are the two arrays you want to multiply.

The following examples illustrate how to perform matrix multiplication for matrices of various sizes.

Matrix Multiplication: (2×2) by (2×2)

Suppose we have a 2×2 matrix C, which has 2 rows and 2 columns:

Suppose we also have a 2×2 matrix D, which has 2 rows and 2 columns:

Here is how to multiply matrix C by matrix D:

This results in the following 2×2 matrix:

Here is how to perform the equivalent matrix multiplication in Excel:

Step 1: Enter the data values for the two matrices. 

Step 2: Multiply the matrices.

  • First, highlight a 2×2 group of cells where the output will go. For example, highlight cells G2:H3
  • With the cells highlighted, type in =MMULT(A2:B3, D2:D3), then click Ctrl+Shift+Enter.

The following results will appear:

2x2 by 2x2 matrix multiplication in Excel

Note: It’s important to click Ctrl+Shift+Enter instead of just Enter after you type in the formula =MMULT(A2:B3, D2:D3), otherwise a single value of “39” will appear in cell G2 without the other three values.

Matrix Multiplication: (2×2) by (2×3)

Suppose we have a 2×2 matrix C, which has 2 rows and 2 columns:

Suppose we also have a 2×3 matrix D, which has 2 rows and 3 columns:

Here is how to multiply matrix C by matrix D:

This results in the following 2×3 matrix:

Here is how to perform the equivalent matrix multiplication in Excel:

Step 1: Enter the data values for the two matrices. 

Step 2: Multiply the matrices.

  • First, highlight a 2×3 group of cells where the output will go. For example, highlight cells H2:J3
  • With the cells highlighted, type in =MMULT(A2:B3, D2:F3), then click Ctrl+Shift+Enter.

The following results will appear:

2x2 by 2x3 matrix multiplication in Excel example

Note: It’s important to click Ctrl+Shift+Enter instead of just Enter after you type in the formula =MMULT(A2:B3, D2:F3), otherwise a single value of “39” will appear in cell H2 without the other values.

Matrix Multiplication: (3×3) by (3×2)

Suppose we have a 3×3 matrix C, which has 3 rows and 3 columns:

Suppose we also have a 3×2 matrix D, which has 3 rows and 2 columns:

Here is how to multiply matrix C by matrix D:

This results in the following 3×2 matrix:

Here is how to perform the equivalent matrix multiplication in Excel:

Step 1: Enter the data values for the two matrices. 

Step 2: Multiply the matrices.

  • First, highlight a 3×2 group of cells where the output will go. For example, highlight cells H2:I4
  • With the cells highlighted, type in =MMULT(A2:C4, E2:F4), then click Ctrl+Shift+Enter.

The following results will appear:

Note: It’s important to click Ctrl+Shift+Enter instead of just Enter after you type in the formula =MMULT(A2:B3, D2:F3), otherwise a single value of “19” will appear in cell H2 without the other values.

Potential MMULT() ERRORS

Note that there are a couple ways you may get an error using the MMULT() function.

Error 1: The rows and columns are not compatible for matrix multiplication.

To multiply two matrices together, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

For example, we can multiply the following matrices together because the first matrix has three columns and the second matrix has three rows:

However, we can not multiply the following matrices together because the first matrix has three columns while the second matrix only has two rows:

If we attempt to use MMULT() to multiply these two matrices together, we will get a #VALUE! error.

Error 2: Something other than a number is used in the matrices.

If characters are used instead of numbers, we will also get a #VALUE! error.

For example, if we attempt to use MMULT() to multiply the following two matrices together, we will get a #VALUE! error:

The “three” in cell C3 needs to be changed to the numerical value 3:

Additional Resources

Matrix Multiplication: (2×2) by (2×2)
Matrix Multiplication: (2×2) by (2×3)
Matrix Multiplication: (3×3) by (3×2)

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