Is the product of two elementary matrices always an elementary matrix? Explain, giving a counterexample if it is not always the case.

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26-10-2022
Mathematics

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Is the product of two elementary matrices always an elementary matrix? Explain, giving a counterexample if it is not always the case.

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rafikiedu08 rafikiedu08 · Answer 1 · 2022-10-27T15:06:28-04:00

The Form B=UA. Let A be an m×n matrix and let B be the reduced row-echelon form of A. Then we can write B=UA where U is the product of all elementary matrices representing the row operations done to A to obtain B

Elementary matrix is obtained from identity matrix by a single elementary row ( or column )

The product of two elementary matrices need not always be an elementary matrix.

example

consider two elementary matrices of order 2

For more explanation i have attached a pic

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