Answer:
12
Step-by-step explanation:
A matrix is diagonal if

In other words, you want non-zero elements only when the indices of the row and the column are the same: the first element of the first row must be non zero, the second element of the second row must be non-zero, and so on. All other elements must be zero.
The answer to this is 36.
Let H be the number hats and J the number of jackets. Then, we can write,

Now, since they want 250 items at least, we can write

Hence, the system of inequalities is