Understanding Isomorphisms for Linear Transformations

[says]

Homework Statement

I have a question about isomorphisms -- I'm not sure if this is the right forum to post this in though.

A linear transformation is an isomorphism if the matrix associated to the transformation is invertable. This means that if the determinant of a transformation matrix = 0, then the transformation is not invertable and thus not an isomorph.

Just wondering if this statement / conclusion is correct? Thanks :)

Homework Equations

The Attempt at a Solution

 

[Samy_A]

Homework Statement

I have a question about isomorphisms -- I'm not sure if this is the right forum to post this in though.

A linear transformation is an isomorphism if the matrix associated to the transformation is invertable. This means that if the determinant of a transformation matrix = 0, then the transformation is not invertable and thus not an isomorph.

Just wondering if this statement / conclusion is correct? Thanks :)

Homework Equations

The Attempt at a Solution

Looks correct (as you talk about matrices, the implicit assumption is that we are talking about a finite dimensional vector space).

EDIT: there is a typo: it must be invertible.