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In this program

Axiomatic characterization of the determinant
Existence
Uniqueness
Det(AB) = det(A)det(B)
Invertibility criteria
Geometric interpretation via signed volume

Determinants (theory)

Det(AB) = det(A)det(B)

Linear algebra · Standard syllabus

Topic

Det(AB) = det(A)det(B)

Practice by unit: Determinants (theory)

Undergraduate Linear Algebra — scope drawn from Axler Linear Algebra Done Right (open PDF), Treil Linear Algebra Done Wrong, Beezer A First Course in Linear Algebra, and AIM-approved OER texts.

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