QJEEM22Madbb6: JEE Main 2022 Mathematics - Class 11 JEEM22Madbb6 Solution: Let A be a 3 3 matrix having entries from the set { 1, 0, 1}.…

Case-I:

$\begin{aligned} 1 & \rightarrow 7 \text { times } \\\\ \text { and }-1 & \rightarrow 2 \text { times } \end{aligned}$

number of possible marrix $=\frac{9 !}{7 ! 2 !}=36$

Case-II:

$1 \rightarrow 6$ times,

$-1 \rightarrow 1$ times

and $0 \rightarrow 2$ times

number of possible marrix $=\frac{9 !}{6 ! 2 !}=252$

Case-III:

$1 \rightarrow 5$ times,

and $0 \rightarrow 4$ times

number of possible marrix $=\frac{9 !}{5 ! 4 !}=126$

Hence total number of all such matrix $A$ $=414$