JEE Main 2021 (Online) 25th July Morning ShiftQuestion 1
Let $M=\left\{A=\begin{pmatrix}a&b\\c&d\end{pmatrix}:a,b,c,d\in\{\pm3,\pm2,\pm1,0\}\right\}$. Define $f:M\to\mathbf{Z}$, as $f(A)=\det(A)$, for all $A\in M$, where $\mathbf{Z}$ is set of all integers. Then the number of $A\in M$ such that $f(A)=15$ is equal to $\_\_\_\_\_\_$ .
Matrices
Answer$16$
Solution
$ad-bc=15$ with entries in $[-3,3]$: $ad=9,bc=-6$ gives $2\cdot4=8$ and $ad=6,bc=-9$ gives $4\cdot2=8$, total $16$.