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How does the zero matrix behave in matrix addition?

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vector parallelogram for addition and subtraction — linear algebra One method of adding and subtracting vectors is to place their tails together and then supply two more sides to form a parallelogram. The vector from their tails to the opposite corner of the parallelogram is equal to the sum of the original vectors. The vector between their heads (starting from the vector being subtracted) is equal to their difference.

In linear algebra, a zero matrix (or null matrix) is defined as a matrix in which every element is 0.

When performing matrix addition, the zero matrix acts as the additive identity. If $B$ is any matrix and $O$ is the zero matrix of the same dimensions, the following property holds true:

$B + O = O + B = B$

In this sense, the zero matrix behaves in matrix addition exactly like the number 0 does in ordinary arithmetic.1