A is square matrix and I is identity matrix of same order and A^3=0 then inverse of I-A
Answers
Answer:
Determinant of a Square Matrix
A determinant could be thought of as a function from Fn� n to F: Let A = (aij) be an n� n matrix. We define its determinant, written as
,
by
.
where Sn is the group of all n! permutations on the symbols{1,2,3,4,...,n} and sgn (s ) for a permutation s Î Sn is defined as follows: Let s written as a function be
.
Let Ni (1 � i < n) denote the number of indices j > i, for which s (j) < s (i), and let N(s ) = S 1� i<n Ni. Ni is called the number of inversions in the permutation s corresponding to the index i, and N is called the total number of inversions in the permutation s . Finally, we define sgn (s ) by the relation sgn (s) � (-1)N(s ) . Thus, sgn (s ) is +1, or -1 according as N(s ) is even, or odd, and accordingly, we call the permutation itself to be even, or odd permutation.
The above notion of determinant remains useful in many more
ha ha ha ha ha ha ha ha ha ha ha