1. ## Identity Matrix

will like to find out that if i have a n * n matrix with the main diagonal all N and the rest of element is 0.

Can i say the determinant is N^n ? or is the determinant is N * I ?

Thanks

2. The determinant of a matrix is a number, not a matrix.

What you have is a diagonal matrix and its determinant is simply the product of all entries along the main diagonal.