To verify whether a matrix B is the inverse of the given matrix A, we need to check whether the product of the two matrices is equal to the identity matrix I. You can use a spreadsheet to find the product of two matrices. A=  1 2 3 2 5 3 1 0 8 B=  -40 16 9 13 -5 -3 5 -2 -1 Using the spreadsheet below (double-click the spreadsheet to open it), verify whether matrix B is the inverse of matrix A. Follow these steps to find the product: Enter the matrices into the spreadsheet below (this has been done for you). Note that matrix A is in cells A2:C4 and matrix B is in cells E2:G4. Both matrices have three rows and three columns, so the product will also be a 3 × 3 matrix. Highlight a 3 × 3 block of cells where you want your answer to appear. Keeping the cells highlighted, enter this formula: =MMULT (A2:C4, E2:G4) Hold down the Shift and Ctrl keys and simultaneously press Enter. The result will appear in the highlighted cells.   Matrix A       Matrix B     1 2 3   -40 16 9   2 5 3   13 -5 -3   3 0 8   2 -2 -1                         Matrix C = A x B                                                                         Since the product of A and B is equal to I, the identity matrix, matrix B is the inverse of matrix A.

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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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To verify whether a matrix B is the inverse of the given matrix A, we need to check whether the product of the two matrices is equal to the identity matrix I. You can use a spreadsheet to find the product of two matrices.

A= 

1 2 3
2 5 3
1 0 8

B= 

-40 16 9
13 -5 -3
5 -2 -1

Using the spreadsheet below (double-click the spreadsheet to open it), verify whether matrix B is the inverse of matrix A. Follow these steps to find the product:

  • Enter the matrices into the spreadsheet below (this has been done for you). Note that matrix A is in cells A2:C4 and matrix B is in cells E2:G4.
  • Both matrices have three rows and three columns, so the product will also be a 3 × 3 matrix. Highlight a 3 × 3 block of cells where you want your answer to appear.
  • Keeping the cells highlighted, enter this formula: =MMULT (A2:C4, E2:G4)
  • Hold down the Shift and Ctrl keys and simultaneously press Enter. The result will appear in the highlighted cells.
  Matrix A       Matrix B    
1 2 3   -40 16 9  
2 5 3   13 -5 -3  
3 0 8   2 -2 -1  
               
      Matrix C = A x B      
               
               
               
               

 

Since the product of A and B is equal to I, the identity matrix, matrix B is the inverse of matrix A.

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