## Related questions with answers

Question

If $A$ is an $n \times n$ matrix with every entry an odd integer, explain why $\operatorname{det} A$ must be divisible by $2^{n-1}$.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 8We make use of the fact that if $i$-th row is added to $j$-th row of a matrix, then determinant does not change. For a proof see exercise $37(b)$. We use induction on $n$ to prove our claim.

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