## MINVERSE Function in Excel

MINVERSE in Excel stands for “Matrix Inverse”. This built-in excel function converts the given matrix to the inverse matrix with the same number of arrays.

Having talked about the “inverse matrix” one needs to understand what exactly the “inverse matrix” is all about.

**Inverse Matrix: **The reciprocal of a number is called the “inverse matrix”. For example, for number 5, we can write the reciprocal as

So, the inverse matrix can be written in the same logic by using this equation ** “A^{-1}”** and the above number can be written as

**as well. When we multiply a number by its reciprocal we always get**

*5*^{-1}**1**as the result. For example, the number 5 is multiplied with its reciprocal 1/5 we get the result as 13

Similarly, when we multiply a matrix by its inverse we get the identity matrix i.e. “I”. Below is the equation of the identity matrix.

**A * A ^{-1} = I**

When we talk about the inverse matrix in excel we need to look at the identity matrix as well. With identity matrix all the number of rows and columns are in equal numbers, with diagonally we get 1 as the value and apart from diagonal everything else will equal to zero.

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So, the identity matrix will always be in the form of ** “2 * 2, 3 * 3, 4 * 4”** like this.

Once the matrix is inversed we can cross-check whether it is inverted or not by using MMULT function in excel and we will get an identity matrix and it looks like this.

Ok, let’s try these things with excel now.

### Example to use MINVERSE Excel Function

For example, take a look at the below 3 * 3 matrix.

- We have matrix numbers from A2 to C4, to reverse this matrix create an identical table next to the above table but do not keep the same values and keep the field empty.

- In the range E2 to G4 we are going to create an inverse of the matrix. Select the range of cells from E2 to G4.

- Now in the selected range of cells open excel MINVERSE function.

- The first argument of MINVERSE function is
**array**i.e. this nothing but the range of matrix values that we are trying to inverse, so our 3 * 3 matrix values are in the range of A2 to C4.

Before we close the formula one thing we need to keep in mind is “MINVERSE” is an array so we need to close out the formula by using “CSE” keys.

**Note:**CSE stands for

**. So all the array formulas are closed with these keys only.**

*“Ctrl + Shift + Enter”*- So, close the formula by hitting ENTER key by holding the “Ctrl + Shift” key together.

As you can see above we have got an “inverse matrix” by using MINVERSE function. Since it is an array formula we can see curly brackets **({})** at the start and end of the array formula.

Now we can cross-check whether this matrix is inversed or not by using MMULT function. MMULT function stands for “Matrix Multiplication”.

- Now select the range of cells to create another identity matrix, so select the 3 * 3 matrix area.

- Now Open MMULT function for the selected range of cells.

- For the
**array1**argument of MMULT function choose “Matrix 1” range from A2 to C4.

- For
**array2**argument of MMULT function choose the “Inverse Matrix” range of cells from E2 to G4.

- MMULT is also an array function, so close the formula by using “CSE” keys to convert to array function.

- This result has given us decimal results, so use the ROUND function inside the array function to get an accurate “identity matrix”.

Now we have got an “identity matrix” where we have 1 as the diagonal value. Like this, we can use MINVERSE function to inverse the matrix and MMULT to check whether it is reversed or not.

### Things to Remember

- MINVERSE function can accept only one matrix at a time.
- This is an array function in excel so use “CSE” keys to close the formula.
- When the matrix is inverse we can find the identity matrix by using MMULT function where we need to multiply the original matrix with the inverse matrix.

### Recommended Articles

This has been a guide to MINVERSE in Excel. Here we learn how to use the MINVERSE function to inverse the matrix and by using Round and MMULT formula to get the identity matrix along with example and downloadable excel template. You may learn more about excel from the following articles –

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