Matrix Determinant So I'm reading through my linear algebra textbook to review for my final, and happened upon this statement:

The determinant of a matrix with positive entries must be positive.

Off the top of my head, I can think of an exception to this:
$$A=\begin{bmatrix}1 & 2\\8 & 3\end{bmatrix}$$
where $\det A= (1\cdot 3) - (2\cdot 8) = 3 - 16 = -13$
Am I misinterpreting what I am reading, or is this a misprint?
The book is Elementary Linear Algebra, 2nd ed. by Spence, Insel, Friedberg
 A: The book is wrong.
Take any square matrix with size $\ge2$ and all entries positive. If its determinant is positive, interchange any two rows. Then the determinant will become negative. So, it is always possible to obtain a negative-determinant matrix with positive entries from a positive-determinant one with positive entries.
A: The sentence, applied to square matrices - in general - is wrong: This must be a misprint, unless the sentence appears in a specific context with other qualifications you may have left out.  
For example, if the discussion is about square triangular matrices, whose non-zero entries are all positive (or with only positive entries on the diagonal), then the statement is true. 
So, since I haven't the text to refer to, to examine at what point in the text, and in what context, the sentence appears, I cannot say for sure. 
But if it is a global statement about the determinant of all square matrices with all positive entries, then the sentence is blatantly not true.
A: My guess is that the book was referring to positive-definite matrices, which are often just called "positive matrices".  This is not the same as having all positive entries.  The simplest definition of positive-definite for matrices is that all the eigenvalues are positive. In this case, it is clear that the determinant is also positive, since the determinant of a matrix is the product of its eigenvalues (counted with algebraic multiplicities).  
A: I think the book has a misprint because the sentence, applied to square matrices in general is false.
