jee-main 2023 Q75

jee-main · India · session1_31jan_shift2 Matrices Determinant and Rank Computation
Let $A = [a_{ij}]$, $a_{ij} \in Z \cap [0,4]$, $1 \leq i, j \leq 2$. The number of matrices $A$ such that the sum of all entries is a prime number $p \in (2, 13)$ is $\_\_\_\_$.
Let $A = [a_{ij}]$, $a_{ij} \in Z \cap [0,4]$, $1 \leq i, j \leq 2$. The number of matrices $A$ such that the sum of all entries is a prime number $p \in (2, 13)$ is $\_\_\_\_$.