Properties of matrix addition  Matrices
Properties of matrix addition
Lessons
Notes:
Let the matrices $X,Y$ and $Z$ have equal dimensions. Then we have the following matrix addition properties:
Dimension property for addition
If $X$ and $Y$ has the same dimensions, then $X+Y$ also has the same dimensions.
Commutative property
$X+Y=Y+X$
Associative property
$(X+Y)+Z=X+(Y+Z)$
There are also some matrix addition properties with the identity and zero matrix.
Property for the zero matrix
There is always a zero matrix $O$ such that $O+X=X$ for any matrix $X$.
Property for the identity matrix
Let $X$ be a $n$ by $n$ matrix. Then there is an identity matrix $I_n$ such that $I_n \cdot X=X$.

2.
Verifying the matrix addition properties
You are given that and and . Verify the following properties: 
3.
You are given that and and . Verify the following properties: