Proving A is Zero Matrix if B is Invertible & Same Size as A

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SUMMARY

If A and B are square matrices of the same size and B is an invertible matrix, then A must be the zero matrix. This conclusion is derived from the property that if the product of two matrices equals the zero matrix (AB = 0), and one of the matrices (B) is invertible, then the other matrix (A) must necessarily be the zero matrix. This relationship is fundamental in linear algebra and is crucial for understanding matrix operations and their implications.

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  • Understanding of square matrices and their properties
  • Knowledge of matrix multiplication and the zero matrix concept
  • Familiarity with invertible matrices and their characteristics
  • Basic linear algebra concepts
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  • Study the properties of invertible matrices in linear algebra
  • Learn about the implications of matrix multiplication resulting in the zero matrix
  • Explore proofs related to matrix equations and their solutions
  • Investigate applications of zero matrices in various mathematical contexts
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Students and professionals in mathematics, particularly those studying linear algebra, as well as educators looking to explain matrix properties and relationships.

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Show that if A and B are square matrices of the same size such that B is an
invertible matrix, then A must be a zero matrix.
 
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blueman11 said:
Show that if A and B are square matrices of the same size such that B is an
invertible matrix, then A must be a zero matrix.
We need information about how A and B are related. ie. AB = 0 or something.

-Dan
 

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