If A is 3x3 with all entries 1's and 0's, what is the max value of det(A)?
I answered it to be 1, which is wrong. Can someone help me?
Thanks!
$\displaystyle A=\begin{bmatrix}a&b&c\\ d&e&f\\ g&h&i\end{bmatrix}$
Use Laplace's formula on the first row and you'll get
$\displaystyle \det(A)=a(ei-fh)-b(di-fg)+c(dh-eg)$
since each entry can only be either 1 or 0, just try to find the coefficients such that you are always summing and not subtracting. You will find that the answer to your question is 2.