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the determinant of the identity matrix?
i need to prove that the determinent of any sized identity matrix is 1 any ideas on how to do this?
references appritiated (if book references 5 stars given)
when i said any i meant the general case, i.e. for all identitiy matrices
3 Answers
- ?Lv 71 decade agoFavorite Answer
if you know that:
det(AB) = det(A)det(B) this is easy:
det(I^2) = (det(I))^2
but I^2 = I, so det(I) = det(I)^2.
let x = det(I). then we have x^2 = x
since I is invertible, x ≠ 0, so we can divide by x to get:
x = 1.
- 1 decade ago
let identity matrix of size 2 X 2
now determinant = a11 * a22 - a12 * a21 = 1 . 1 - 0.0 =1-0=1
