1. Tardigrade
  2. Question
  3. Mathematics
  4. The number of matrices of order 3 × 3, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The number of matrices of order $3 \times 3$, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is

JEE MainJEE Main 2022Matrices

Solution:

$A =\begin{bmatrix} a _{11} & a _{12} & a _{13} \\ a _{21} & a _{22} & a _{23} \\ a _{31} & a _{32} & a _{33}\end{bmatrix}a _{ ij } \in\{0,1\}$
$ \sum a _{ ij }=2,3,5,7 $
Total matrix $={ }^9 C _2+{ }^9 C _3+{ }^9 C _5+{ }^9 C _7$
$=282$