A transpose of a nonsingular matrix is nonsingular

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Homework Help Overview

The discussion revolves around the property of the transpose of a nonsingular matrix and its nonsingularity, specifically seeking a proof or explanation that does not involve determinants.

Discussion Character

  • Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to explore the property of transposes without relying on determinants, indicating a desire for alternative reasoning. Another participant suggests using the property of the transpose of a product of matrices.

Discussion Status

The discussion has seen some engagement, with a participant providing a potential approach related to matrix multiplication properties. However, the original poster's request for non-determinant methods suggests that further exploration may still be needed.

Dustinsfl
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A transpose of a nonsingular matrix is nonsingular.

This is true; however, how can this be done without using determinants?

I know how to do this with determinants so please don't inform how to do this with determinants.
 
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Use (AB)T = BTAT
 


Thanks got it.
 


:smile:
 

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