M inverse

MINVERSE Function

The MINVERSE function in Excel calculates the inverse of a square matrix provided as an array or range. The inverse of a matrix ( A ) is a matrix ( B ) such that ( A \times B = I ), where ( I ) is the identity matrix.

Syntax:

MINVERSE(array)

• array: A square range of cells (e.g., A1:B2) or a 2D array constant that represents a matrix. The number of rows and columns must be equal.

Examples:

1. 2x2 Matrix
   If the range A1:B2 contains:

   4   7  
   2   6  
   

   Formula: =MINVERSE(A1:B2)
   Returns:

   0.6   -0.7  
   -0.2   0.4  
   

   Explanation: This is the inverse of the 2x2 matrix.

2. 3x3 Matrix
   If the range A1:C3 contains:

   1   2   3  
   0   1   4  
   5   6   0  
   

   Formula: =MINVERSE(A1:C3)
   Returns:

   -24    18   5  
   20    -15   -4  
   -5     4    1  
   

   Explanation: Excel calculates the inverse of the 3x3 matrix.

3. Single-Cell Matrix
   If A1 contains 5:
   Formula: =MINVERSE(A1)
   Returns: 0.2, because the inverse of a 1x1 matrix is ( 1 / \text{value} ).

Usage Notes:

• The input must be a square matrix; Excel will return a #VALUE! error if the rows and columns are not equal.
• If the determinant of the matrix is 0 (i.e., the matrix is singular), Excel will return a #NUM! error because the matrix does not have an inverse.
• The MINVERSE function must be entered as an array formula in versions prior to Excel 365:
  • Select a range with the same dimensions as the original matrix.
  • Enter the formula and press Ctrl + Shift + Enter.
• In Excel 365 and Excel 2021, dynamic arrays allow the result to spill automatically without Ctrl + Shift + Enter.
• All elements in the input matrix must be numeric; otherwise, Excel will return an error.
• The inverse matrix is widely used in linear algebra to solve systems of linear equations and other mathematical computations.