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Suppose that A is a product of elementary matrices E1,...,En. Then the inverses of elementary
matrices ,the matrices E1,...,En are invertible. By the first theorem about inverses the product of
invertible matrices is an invertible matrix. So A is an invertible matrix as A is the product of
elementry matrices.

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prove thisSolutionSuppose that A is a product of element.pdf

  • 1. prove this Solution Suppose that A is a product of elementary matrices E1,...,En. Then the inverses of elementary matrices ,the matrices E1,...,En are invertible. By the first theorem about inverses the product of invertible matrices is an invertible matrix. So A is an invertible matrix as A is the product of elementry matrices.