Mathematics - Matrices Question with Solution | TestHub

Let $A_n,(n\in N)$ be a matrix of order $(2n-1)\times (2n-1)$, such that $a_{ij}=0\forall i\ne j$ and $a_{ij}=n^2+i+1-2n\forall i=j$ where $a_{ij}$ denotes the element of $i^{\text{th }}$ row and $j^{\text{th }}$ column of $A_n$. Let $T_n=(-1{)}^n\times$ (sum of all the elements of $A_n$ ). Find the value of $\left[\frac{{\sum }_{n=1}^{102}{T}_n}{520200}\right]$, where [.] represents the greatest integer function.