If `A=[0 1 0 0]` , prove that `(a I+b A)^n=a^n\ I+n a^(n-1)\ b A` where `I` is a unit matrix of order 2 and `n` is a positive integer.

Let A=[[0,10,0]] show that (aI+bA)^(n)=a^(n)I+na^(n-1)bA where I is the identity matrix of order 2 and n in N

If I is unit matrix of order n, then 3I will be

((1+i)/(1-i))^(4n+1) where n is a positive integer.

If I_(n) is the identity matrix of order n then (I_(n))^(-1)=

Prove that 2^(n)>1+n sqrt(2^(n-1)),AA n>2 where n is a positive integer.

Minimum value of n for which (2i)^n/(1-i)^(n-2) is positive integer

If A is a non zero square matrix of order n with det(I+A)!=0 and A^(3)=0, where I,O are unit and null matrices of order n xx n respectively then (I+A)^(-1)=

If ((1+i)/(1-i))^x=1 then (A) x=2n+1 , where n is any positive ineger (B) x=4n , where n is any positive integer (C) x=2n where n is any positive integer (D) x=4n+1 where n is any positive integer

Find the least positive integer n such that ((2i)/(1+i))^(n) is a positive integer.

If A=[[a,b],[0,1]] then prove that A^n=[[a^n,(b(a^n-1))/(a-1)],[0,1]]