Properties of Zero Matrix

Theorem

Let

• $c$ : Scalar
• $A$ : Matrix
• $0$ : Zero matrix

Suppose sizes of $A$ and $0$ are such that the operations can be performed

Then

• $A+0=0+A=A$
• $A-0=A$
• $A-A=A+(-A)=0$
• $0A=0$
• $cA=0⟹c=0\vee A=0$