If $a, b, c$ are real numbers such that $a^2+b^2+c^2-ab-bc-ac\le 0,$ then

$\left|\begin{array}{ccc}(a-b+1{)}^5& b^7-c^7& c^9-a^9\\ a^{11}-b^{11}& (b-c+2{)}^3& c^{13}-a^{13}\\ a^{15}-b^{15}& b^{17}-c^{17}& (c-a+3{)}^1\end{array}\right|=$

The remainder when the value of the determinant $\left|\begin{array}{lll}{2014}^{2014}& {2015}^{2015}& {2016}^{2016}\\ {2017}^{2017}& {2018}^{2018}& {2019}^{2019}\\ {2020}^{2020}& {2021}^{2021}& {2022}^{2022}\end{array}\right|$ is divided by $5$ is

Let $A$ be a $2\times 2$ real matrix with entries from $\left\{0, 1\right\}$ and $\left|A\right|\ne 0$. Consider the following two statements;

$\left(P\right)$ If $A\ne I_2$, then $\left|A\right|=-1$

$\left(Q\right)$ If $\left|A\right|=1$, then $tr\left(A\right)=2$

Where $I_2$ denotes $2\times 2$ identity matrix and $tr\left(A\right)$ denotes the sum of the diagonal entries of $A$. Then