Let A be a square matrix of order $3$ with integer entries such that $\det(A)=1$. 
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*What is the maximum possible number of entries of A that  are  even? What if A is a matrix of order n?

*What is the maximum possible number of entries of A that  are  PRIMES? What if A is a matrix of order n?
This question was asked  during my class test and I was unable to do this.
Please help me in doing this.

For the first question, you can show that $I_3$ is an example of such a matrix with $6$ even entries. If there are $7$ or more event entries, then necessarily there is a row with only even entries, calculate your determinant by expanding this line, it is a sum of even terms, thus the determinant is even and can't be $1$.
Thus $6$ is the maximum possible number of entries of A that are even and such as $\det(A)=1$.

The generalisation for matrices of order $n$, for the first question is $n^2-n$, you can prove this with same reasoning that in the case $3 \times 3$ : $I_n$ has $n^2-n$ even entries and its determinant is $1$. And if your matrix has more that $n^2-n$ even entries then there is necessary a whole row with even entries and you can expand your determinant from this row and thus it will be even and so different of $1$.
