When we evaluate it at the identity matrix we get 1, therefore it is equal to the determinant. ![]() When n is equal to r, the equation gets reduced to n which is a simple factorial of n. The formula for permutation of n objects for r selection of objects is given by: P(n,r) n/(n-r) For example, the number of ways 3rd and 4th position can be. Permutations are useful to form different words, number arrangements, seating arrangements, and for all the situations involving different arrangements. Since every term is cancelled by another term, the form evaluates to 0, hence it is alternating and therefore a multiple of the determinant. Combinations have no regard for this while permutations do. The permutation formula is used to find the different number of arrangements that can be formed by taking r things from the n available things. ![]() Many people (in different texts) use the following famous definition of the determinant of a matrix $A$: \begin$, this exactly cancels the term coming from $\sigma$.
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