Recall: Theorem: The matrix addition is associative that is let A,B,C be matrices of order M x n. Then, \((A+B)+C=A+(B+C)\).

Theorem: The matrix addition is commutative that is let A and B be matrices of order M x n. Then \(A+B=B+A\).

The given matrix is, \(A=[1,2,4,3]\).

We have to find a matrix B such that \(A+B=0\), where 0 is the zero matrix. Now,

\(A+B=0\)

\(\displaystyle\to{B}+{A}={0}\)

\(\displaystyle\to{\left({B}+{A}\right)}-{A}={0}-{A}\)

\(\displaystyle\to{B}+{\left({A}-{A}\right)}=-{A}\)

\(\displaystyle\to{B}+{0}=-{A}\)

\(\displaystyle\to{B}=-{A}\)

\(\displaystyle\to{B}=-{\left[{1},{2},{4},{3}\right]}\)

\(\rightarrow B=[-1,-2,-4,-3]\)

Therefore, when \(A=[1,2,4,3]\), for \(B=[-1,-2,-4,-3], A+B=0\).