Practice question · Match the pairs
Match each determinant property to its statement.
- det(AB)
- det(Aᵀ)
- for n
- ·
- 1/det(A)
- det(A)
- cⁿ det(A)
Hints
- Ask how each operation on rows affects the value.
- Swapping two rows changes something that scaling does not.
Show the answer
- det(AB) → ·
- det(Aᵀ) → det(A)
- for n → cⁿ det(A)
- → 1/det(A)
Why
These properties make determinant calculations more efficient.
Practise Determinants
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More questions on Determinants
- Which statements are true when det(A) = 0?
- Sort these determinant values into Invertible or Singular.
- A 2×2 matrix M has det M = 0. It transforms the plane. What does it do to the unit square?
- The determinant’s absolute value is the factor by which a transformation scales area or volume. What does a…
- If det(A) = 0, then A is invertible.