If AB=I, then A is invertible. False

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Homework Help Overview

The discussion revolves around the properties of matrices, specifically addressing the statement "If AB=I, then A is invertible." Participants are exploring the conditions under which this statement holds true, particularly in relation to the dimensions of the matrices involved.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants present examples of non-square matrices that yield a product equal to the identity matrix, questioning the necessity of square matrices for invertibility. Others inquire about the implications of the dimensions of matrices A and B on the invertibility of A.

Discussion Status

The discussion is active, with participants sharing examples and raising questions about the assumptions related to matrix dimensions and invertibility. Some have expressed uncertainty about how to formally demonstrate their points.

Contextual Notes

There is a focus on the dimensionality of matrices, with specific mention of 2x3 and 3x2 matrices, and the implications for invertibility when the product equals the identity matrix. Participants are navigating the constraints of matrix properties without reaching a consensus.

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If AB=I, then A is invertible.

False, but not sure how to show it.
 
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Dustinsfl said:
If AB=I, then A is invertible.

False, but not sure how to show it.
There's no requirement that A and B have to be square matrices. I came up with a 2x3 matrix and a 3x2 matrix whose product is I, a 2x2 matrix, yet neither of the matrices in the product is invertible.
 
Thanks, I figured out a matrix that works.
 
If A(n*n) and B (n*n).
and If AB=I.
is A invertible?
is B inverse of A?
 
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