Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statemen

a) False.
The addition of Matrices is Commutative.
For example:
Consider two matrices, of order
$A=[[1,3],[2,4]],B=[[0,1],[-1,4]]$
Matrices A and B are commutative under addition, if, A+B=B+A
$\Rightarrow [[1,3],[2,4]]+[[0,1],[-1,4]]=[[0,1],[-1,4]]+[[1,3],[2,4]]$
$\Rightarrow [[1,4],[1,8]]=[[1,4],[1,8]]$
Hence Commutative.
b) True.
Yes, The transpose of the sum of matrices is equal to the sum of the transposes of the matrices.
Consider two matrices, of order $2\times 2$
$A=[[1,3],[2,4]],B=[[0,1],[-1,4]]$
$A+B=[[1,4],[1,8]]$
$\Rightarrow (A+B{)}^{\prime }=[[1,1],[4,8]]$ (1)
$A^{\prime }=[[1,2],[3,4]]$
$B^{\prime }=[[0,-1],[1,4]]$
$A^{\prime }+B^{\prime }=[[1,2],[3,4]]+[[0,-1],[1,4]]$
$\Rightarrow A^{\prime }+B^{\prime }=[[1,1],[4,8]]$ (2)
Drom (1) and (2)
(A+B)'=A'+B'
Hence proved