Answer
The ij-th entry of the sum of A and B = sum of their ij-th entries
Work Step by Step
$M_{ij}$ is the element of matrix M at its ith row, jth column.
or, as we say in short, the ij-th entry.
$A+B$ is a matrix,
$(A+B)_{ij}$ is the entry at its ith row, jth column.
$(A+B)_{ij}=A_{ij}+B_{ij}$
means
The ij-th entry of the sum of A and B = sum of their ij-th entries
