Home
Class 12
MATHS
If A=[(1,2),(2,1)] show thatA^(2)-3I=2A...

If `A=[(1,2),(2,1)]` show that`A^(2)-3I=2A`

Promotional Banner

Topper's Solved these Questions

  • SELF ASSESSMENT PAPER 9

    ICSE|Exercise SECTION-B|9 Videos
  • SELF ASSESSMENT PAPER 9

    ICSE|Exercise SECTION C|10 Videos
  • SELF ASSESSMENT PAPER 2

    ICSE|Exercise Section - C|12 Videos
  • SPECIMEN QUESTION PAPER

    ICSE|Exercise Section C|8 Videos

Similar Questions

Explore conceptually related problems

If A=[(1,1),(0,1)] , show that A^2=[(1, 2),( 0, 1)] and A^3=[(1 ,3 ),(0 ,1)] .

If A=[(4, 5),( 2 ,1)] , then show that A-3I=2(I+3A^(-1))

If A=[(2, 3),(-1 ,0)] , show that A^2-2A+3I^2=O .

(i) if A=[{:(1,-1),(2,3):}], then show that A^(2)-4A+5I=O. (ii) if f(x)=x^(2)+3x-5and A=[{:(2,-1),(4,3):}], then find f(A).

If A=[(3, 1),(-1 ,2)] , show that A^2-5A+7I=O . Hence, find A^(-1) .

If A=[(3, 1),( 1, 2)] , show that A^2-5A+5I=0 . Hence, find A^(-1) .

If A=[{:(1,2,2),(2,1,2),(2,2,1):}] , then show that A^(2)-4A-5I_(3)=0 . Hemce find A^(-1) .

If A=[(2,-3),(3,4)], show the A^2-6A+17I=0. Hence find A^-1

If M=[{:(,4,1),(,-1,2):}] show that 6M-M^2=9I , where I is a 2 xx 2 unit matrix.

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.