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Q.

The number of matrices of order 3 x 3, whose entries are either 0 or I and the sum of all the entries is a prime number, is_____.

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answer is 282.

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Detailed Solution

$A = {[a_{ij}]}_{3 \times 3}, where a_{ij} \in {0, 1}$
$\sum a_{ij} can be 2, 3, 5, 7$
$∴$ Number of matrices $=^{9} C_{2} +^{9} C_{3} +^{9} C_{5} +^{9} C_{7}$
$= 36 + 84 + 126 + 36 = 282$

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