For all matrices \(A, B, C\), it

• commutes, so

  \(A + B = B + A\),

• associates, so

  \((A + B) + C = A + (B + C)\),

• has exactly one additive identity: the zero matrix, so

  \(A + 0_{m \times n} = A\),

• has exactly one additive inverse: \(-A\), so

  \(A + (-A) = 0_{m \times n}\).