Work out scalar multiplication of matrix instantly with clear inputs, formula shown and shareable results.
Scalar multiplication multiplies every entry by k. For an n × n matrix this scales the determinant by kⁿ, because each of the n rows is scaled independently.
Scalar multiple
(kA)ᵢⱼ = k·Aᵢⱼ
Determinant
det(kA) = kⁿ · det(A) for an n × n matrix
[[3, 6], [9, 12]], and the determinant goes from −2 to 3² × −2 = −18.
The determinant is linear in each row separately, so scaling all n rows multiplies it n times over.