In a compact one dimensional array representation for lower triangular matrix (all elements above diagonal are zero) of size $$n \times n$$, non zero elements of each row are stored one after another, starting from first row, the index of $$(i, j)^{th}$$ element in this new representation is

A

$$i + j$$

B

$$j + \frac{i(i - 1)}{2}$$

C

$$i + j - 1$$

D

$$j + \frac{j(j - 1)}{2}$$