Let $A$ be a $3 imes 3$ matrix which contains five ' $a$ ' & four ' $b$ ' then number of symmetric

Question

Let $A$ be a $3 	imes 3$ matrix which contains five ' $a$ ' & four ' $b$ ' then number of symmetric matrices possible is $k$, number of zeros at the end of $k!$ is $\_\_\_\_$ .

Professor PC Thomas Classes · Answer

$\left(\begin{array}{lll}a & d & e \ d & b & f \ e & f & c\end{array}ight)$ Symmetric matrices Diagonal all ' a, or $1^{\prime} \mathrm{a}, 2^{\prime} \mathrm{b}$
$\left(\begin{array}{lll}a & a & b \ a & a & b \ b & b & a\end{array}ight)$ or $\left(\begin{array}{lll}a & b & a \ b & a & b \ a & b & a\end{array}ight)$ or $\left(\begin{array}{lll}a & b & b \ b & a & a \ b & a & a\end{array}ight)=3$