Home
Class 12
MATHS
if A=[[i,0] , [0,i]] where i=sqrt(-1) an...

if `A=[[i,0] , [0,i]]` where `i=sqrt(-1)` and `x epsilon N` then `A^(4x)` equals to:

Text Solution

Verified by Experts

`A^(2)=[(i,0),(0,i)][(i,0),(0,i)]=[(i^(2),0),(0,i^(2))]=[(-1,0),(0,-1)]`
`A^(4)=[(-1,0),(0,-1)][(-1,0),(0,-1)]=[(1,0),(0,1)]=I`
`implies A^(4n)=I^(n)=I`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise 13.4|12 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.5|17 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.2|6 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

If z=i^(i^(i)) where i=sqrt-1 then |z| is equal to

If x=a+bi is a complex number such that x^2=3+4i and x^3=2+11i , where i=sqrt-1 , then (a+b) equal to

Let (-2 -1/3 i)^3=(x+iy)/27 (i= sqrt(-1)) where x and y are real numbers then y-x equals

Prove that z=i^i, where i=sqrt-1, is purely real.

Let I_n=int tan^n x dx, (n>1) . If I_4+I_6=a tan^5 x + bx^5 + C , Where C is a constant of integration, then the ordered pair (a,b) is equal to :

tan^(- 1)((sqrt(1+a^2x^2)-1)/(a x)) where x!=0, is equal to

If I=int sqrt((5-x)/(2+x)) dx, then equal

If |z-2-i|=|z|sin(pi/4-a r g z)| , where i=sqrt(-1) ,then locus of z, is

Let g(x)=1=x-[x] and f(x)={-1, x < 0 , 0, x=0 and 1, x > 0, then for all x, f(g(x)) is equal to (i) x (ii) 1 (iii) f(x) (iv) g(x)

If I=int(dx)/(x^(4)sqrt(a^(2)+x^(2))) , then I equals