If `k in R_(0)`, then det `{"adj "(kI_(n))}` is equal to

If k in R_ot h e ndet{a d j(k I_n)} is equal to K^(n-1) b. K^(n(n-1)) c. K^n d. k

If A = [(a,x),(y,a)] and if xy = 1, then det ("AA"^(T)) is equal to

If A and B are square matrices of order 3 such that det. (A) = -2 and det.(B)= 1 , then det.(A^(-1)adjB^(-1).adj(2A^(-1)) is equal to

If s_(n) = sum_(r = 0)^(n) 1/(""^(n)C_(r)) and t_(n) = sum _(r = 0)^(n) r/(""^(n)C_(r)) ,then t_(n)/s_(n) is equal to

If A and B are two non-singular matrices of order 3 such that A A^(T)=2I and A^(-1)=A^(T)-A . Adj. (2B^(-1)) , then det. (B) is equal to

If y^r=(n !^(n+r-1)C_(r-1))/(r^n),w h e r en=k r(k is contstant), then ("lim")_(rvecoo)y is equal to (a) (k-1)(log)_e(1+k)-k (b) (k+1)(log)_e(1-k)+k (c) (k+1)(log)_e(1-k)-k (d) (k-1)(log)_e(1-k)+k

If A is an invertible matrix of order 2, then det (A^(-1)) is equal to

If A and B are two invertible matrices of the same order, then adj (AB) is equal to

Let A and B be two invertible matrices of order 3xx3 . If det. (ABA^(T)) = 8 and det. (AB^(-1)) = 8, then det. (BA^(-1)B^(T)) is equal to