DX will contain required sum:
mov dx,0
mov esi,matr
mov ecx,0
mov cx,[dimmatr]
mov eax,1
mRow:
push ecx
mov cx,[dimmatr]
mov ebx,0
mCol:
cmp ebx,eax
jl msk
add dx,word [esi]
msk:
inc ebx
add esi,2
loop mCol
inc eax
pop ecx
loop mRow
dimmatr dw 3;matrix dimension
matr dw 1,1,1,2,2,2,3,3,3;matrix