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Can Somebody Please explain me in detail description how to calculate the number of upper triangular and lower triangular of a square matrix I read somewhere that it turns out to be ((n^2)+n) /2,Can someone please provide me with a proof

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Hope u are clear now 

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gatecse asked Oct 30, 2020
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Let $P = [p_{ij}],$ where $1 \leq i,j \leq n$ is defined by $p_{ij} = i\times j, \forall i,j$ with $n 2.$ The rank of $P$ is _______