- #1
johndoe3344
- 29
- 0
For an n x n matrix A, what is the relationship between det(A) and det(-A)?
I tried it with a 1x1 matrix, and det (-A) = - det (A)
I tried it with a 2x2 matrix, and det(A) = det(-A)
I tried it with a 3x3 matrix, and the results were the same as that with a 1x1.
This leads me to believe that for all odd n's, det(-A) = - det(A) and that for all even n's the two are the same.
Is this the case? And if so, how would I show that in a more mathematical manner that just intuition?
I tried it with a 1x1 matrix, and det (-A) = - det (A)
I tried it with a 2x2 matrix, and det(A) = det(-A)
I tried it with a 3x3 matrix, and the results were the same as that with a 1x1.
This leads me to believe that for all odd n's, det(-A) = - det(A) and that for all even n's the two are the same.
Is this the case? And if so, how would I show that in a more mathematical manner that just intuition?