in Set Theory & Algebra
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3 votes
3 votes
Let A be a $3 \times 3$ matrix with integer entries such that $|A| =1$. What is the maximum possible number of entries of A that are even?
in Set Theory & Algebra
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3 Comments

I am getting 6
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0
explain plz
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Take diagonal elements 1 and rest 0
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1 Answer

2 votes
2 votes

Here $I3$ is the best example for such matrix.

$A = \begin{bmatrix} 1 & 0 & 0\\ 0& 1 & 0\\ 0& 0 & 1 \end{bmatrix}$

Here even number entries are 6 and $|A|=1$.We can't get more than 6 even element for this type of matrix.

Hence,Maximum number of even entries in  A is $6$.

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