Choose the false statement

Vector multiplication (to produce the cross product, i.e., $\mathrm{a}.\mathrm{b}=\mathrm{b}.\mathrm{a}$  and scalar multiplication (to produce the so-called dot product) are not commutative operations .

When conditionally convergent series are multiplied, the commutative law may not always apply$(\mathrm{a}\times \mathrm{b}=\mathrm{b}\times \mathrm{a})$.

Because c (a b) = (c a) b = a, the scalar multiplication property is also known as the "associative law for scalar and dot product" or "the dot product is associative with regard to scalar multiplication" $\mathrm{c}(\mathrm{a}\cdot \mathrm{b})=(\mathrm{c} \mathrm{a})\cdot \mathrm{b}=\mathrm{a}\cdot (\mathrm{c} \mathrm{b})$.

Hence the correct answer is all the above.