What is a zero matrix?

A zero matrix is defined specifically as a matrix in which every single element is zero. This characteristic means that regardless of the size or dimensions of the matrix—whether it is a 2x2, 3x3, or larger—it will not contain any non-zero values. This concept is important in linear algebra as zero matrices serve as the additive identity in matrix addition; adding a zero matrix to any other matrix leaves the other matrix unchanged.

The other definitions do not capture the essence of a zero matrix. Matrices with all elements being one, those with at least one non-zero element, or matrices containing varying elements do not meet the strict criterion of having all elements equal to zero, which is the defining feature of a zero matrix. Understanding this distinction is crucial for grasping matrix operations and their properties.