$$P = \left[ {\matrix{ 1 & 2 & 1 \cr 1 & 3 & 1 \cr } } \right],Q = P{P^T}$$, then the value of determinant of Q is

If $f(x)=\frac{1+x}{1-x}$ and $A$ is a matrix such that $A^3=0$, then $f(A)=$

Let us define the power of a matrix $A$ as the maximum $m \in Z^{+}$such that $A^m=I$. For two matrices $A$ and $B$ if $A^5=I$ and $A B A^{-1}=B^2$, then the power of the matrix $B$ is between

Let $\operatorname{det} A=\left|\begin{array}{ccc}\mathrm{l} & \mathrm{m} & \mathrm{n} \\ \mathrm{p} & \mathrm{q} & \mathrm{r} \\ \mathrm{l} & \mathrm{l} & \mathrm{l}\end{array}\right|$ If $(I-m)^2+(p-q)^2=9,(m-n)^2+(q-r)^2=16,(n-I)^2+(r-p)^2=25$, then the value of $(\operatorname{det} A)^2$ is