不需要A一定是可逆.
知識點:
AA* = |A|E.
|A*| = |A|^(n-1)
當 r(A) = n 時, r(A*) = n
當 r(A) = n-1 時, r(A*) = 1
當 r(A) < n-1="" 時,="" r(a*)="">
證明:
A*(A*)* = |A*|E
AA*(A*)* = |A*|A
|A| (A*)* = |A|^(n-1) A
所以, 當A可逆時, (A*)* = |A|^(n-2) A.
當A不可逆時, |A|=0
r(A) <=>
r(A*)<=>
r((A*)*) = 0
即有 (A*)* = 0 = |A|^(n-2) A
