How many matrices X (3 × 3) with entries (0, 1, 2) are there for which sum of diagonal entries of XX' is 7? and is a three digit number LMN, then the value of  $\frac{M}{L}$ is equal to 

$\left[\begin{array}{l}abc\\ def\\ ghi\end{array}\right]\left[[\begin{array}{l}abc\\ def\\ ghi\end{array}\right]\Rightarrow$ Sum of diagonal
$=\sum a^2$   (all 9 terms of element)
$a^2+b^2+c^2+d^2+e^2+f^2+g^2+h^2+i^2=7$
(5 zero) 1 of them 2, 3 of them  $1\Rightarrow 7={}_{ }{}^{9}C_4\frac{4!}{3!}$
(2 zero) 7 of them $1\Rightarrow 7={}_{ }{}^{9}C_7\frac{7!}{7!}$  
Required value is LMN = 540
there for  $\frac{M}{L}=\frac{4}{5}=0.8$