Final answer:
The statement is true: a linear transformation preserves both vector addition and scalar multiplication, which are essential properties of linear transformations in linear algebra.
Step-by-step explanation:
The statement is true: A transformation is linear if it preserves both addition and scalar multiplication. In the context of vector operations, this means that if T is a linear transformation, then T(u + v) = T(u) + T(v) for any vectors u and v, and T(cu) = cT(u) for any scalar c and vector u. This concept is foundational in linear algebra.
Vector addition is commutative and associative, and scalar multiplication is distributive over vector addition. For example, given vectors A and B, we have A + B = B + A, and for scalars c and d, (c + d)A = cA + dA. These properties are essential for the definition of a linear transformation.