Let A=[aij] be 3×3 matrix given by aij=⎧⎪⎨⎪⎩(i+j2)+|i−j|2,ifi≠jij−(i.j)i2+j2,ifi=j⎫⎪⎬⎪⎭ where aij denotes element of ith row & jth column of matrix A.If A=pA2−qA−1−rI, then remainder when (p+q+r)11 is divided by 7 is

Let A=[aij] be 3×3 matrix given by aij=⎧⎪⎨⎪⎩(i+j2)+|i−j|

1.	Let A=[aij] be 3×3 matrix given by aij=⎧⎪⎨⎪⎩(i+j2)+\|i−j\|2,ifi≠jij−(i.j)i2+j2,ifi=j⎫⎪⎬⎪⎭ where aij denotes element of ith row & jth column of matrix A.If A=pA2−qA−1−rI, then remainder when (p+q+r)11 is divided by 7 is
Answer» Let $A = [a_{i j}]$ be $3 \times 3$ matrix given by $a_{i j} = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} (\frac{i + j}{2}) + \frac{\| i - j \|}{2}, & i f i \neq j \frac{i^{j} - (i . j)}{i^{2} + j^{2}}, & i f i = j \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭$ where $a_{i j}$ denotes element of $i^{t h}$ row & $j^{t h}$ column of matrix A.If $A = p A^{2} - q A^{- 1} - r I$ , then remainder when $(p + q + r)^{11}$ is divided by 7 is