Matrix multiplication is commutative.

A square matrix where every element is unity is called an identity matrix.

If $A$ and $B$ are two square matrices of the same order, then  $A+B=B+A$.

If $A$ and $B$ are two matrices of the same order, then$A-B=B-A$.

Transpose of a column matrix is a column matrix.

If $A$ and $B$ are two square matrices of the same order, then $AB=BA$.

If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.

If $A$ and $B$ are any two matrices of the same order, then $(AB{)}^{\text{'}}=A^{\text{'}}{B}^{\text{'}}$.