If `B_(0)=[(-4, -3, -3),(1,0,1),(4,4,3)], B_(n)=adj(B_(n-1), AA n in N` and I is an identity matrix of order 3, then `B_(1)+B_(3)+B_(5)+B_(7)+B_(9)` is equal to

If A_(0) = [[2 ,-2,-4],[-1,3,4],[1,-2,-3]] and B_(0)= [[-4,-4,-4],[1,0,1],[4,4,3]] and B_(n) = adj (B_(n-1)),n inN and I is an dientity matrix of order 3. B_(2) + B_(3) + B_(4) +...+ B_(50) is equal to

If A_(0) = [[2 ,-2,-4],[-1,3,4],[1,-2,-3]] and B_(0) [[-4,-4,-4],[1,0,1],[4,4,3]] and B_(n) = adj (B_(n-1)),n inN and I is an dientity matrix of order 3. det (A_(0) + A_(0)^(2) B_(0) ^(2) + A_(0)^(2) + A_(0) ^(4) B_(0)^(4) + ... upto 12 terms ) is equal to

If A_(0) = [[2 ,-2,-4],[-1,3,4],[1,-2,-3]] and B_(0) =[[-4,-4,-4],[1,0,1],[4,4,3]] and B_(n) = adj (B_(n-1)),n inN and I is an dientity matrix of order 3. For a variable matrix X, the equation A_(0) X = B_(0) will heve

Let A = ((1,-1,0),(0,1,-1),(0,0,1))andB=7A^(20)-20A^(7)+2I, where I is an identity matrix of order 3 xx 3 if B = [b_(ij)] then b_(13) is equal to __________ .

Let A=[(0,1),(0,0) ] show that (a I+b A)^n=a^n I+n a^(n-1)b A , where I is the identity matrix of order 2 and n in N .

A_(1), A_(2), A_(3), ……, A_(n) " and " B_(1), B_(2), B_(3), …., B_(n) are non-singular square matrices of order n such that A_(1)B_(1) = I_(n), A_(2)B_(2) = I_(n), A_(3)B_(3) = I_(n),……A_(n)B_(n) = I_(n) " then"(A_(1) A_(2)A_(3)….. A_(n))^(-1) = ______.

Let A=[[0, 1],[ 0, 0]] show that (a I+b A)^n=a^n I+n a^(n-1)b A , where I is the identity matrix of order 2 and n in N .

Let A = ((1,2),(3,4)) and B = ((a,0),(0,b)), a b in N . Then :

Let A = [(1,1),(0,1)] and B = [(b_(1),b_(2)),(b_(3),b_(4))] . If 10 A^(10) +Adj (A^(10)) = B then b_(1)+b_(2)+b_(3)+b_(4) is equal to :