Final answer:
To find integer matrices that (1) are not diagonal matrices and (2) have the same determinant, you can consider the example provided.
Step-by-step explanation:
To find integer matrices that (1) are not diagonal matrices and (2) have the same determinant, we can consider the following example:
Let matrix A be:
A = [1 2; 2 4]
The determinant of matrix A is (1 × 4) - (2 × 2) = 0.
Now, let matrix B be:
B = [-4 -2; -2 -1]
The determinant of matrix B is (-4 × -1) - (-2 × -2) = 0.
Both matrices A and B are not diagonal matrices, and they have the same determinant.