Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I'm studying my mathematics lesson, and there is an example I can't understand:

Consider the matrix

A=(0 In)

(-In 0)

with In the identity nxn

We want to compute detA :

We introduce the permutation

p=(1 2 ... n n+1 ... 2n)

(n n+1 ... 2n 1 ... n )

s.t if we apply p to the columns of A, then we get

B=(In 0)

(0 -In)

(so far so good)

then we say: detB=(-1)^n (ok)

the sign of p is (-1)^n (all right)

then detA=(-1)^n*(-1)^n=1...(why???)

Thanks in advance

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# Homework Help: Determinant of a matrix with identity blocks

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