Home
Class 12
MATHS
Let a be a matrix of order 2xx2 such tha...

Let a be a matrix of order `2xx2` such that `A^(2)=O`.
`A^(2)-(a+d)A+(ad-bc)I` is equal to

A

`I`

B

`O`

C

`-I`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let
`A=[(a,b),(c,d)]`
`implies A^(2)-(a+d)A+(ad-bc)I`
`=[(a,b),(c,d)][(a,b),(c,d)]-(a+d)[(a,b),(c,d)]+(ad-bc)[(1,0),(0,1)]`
`=[(a^(2)+bc,ab+bd),(ac+cd,bc+d^(2))]-[(a^(2)+ad,ab+bd),(ac+cd,bc+d^(2))]+[(a^(2)+ad,ab+bd),(ac+cd,ad+d^(2))]`
`=O`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Numerical)|24 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Multiple)|33 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

Write the matrix of the order 2xx1 .

If A is a non singular matrix and I is a unit matrix of order same as A such that A^(2)+A-I=O , then A^(-1) is equal to

Knowledge Check

  • Let a be a matrix of order 2xx2 such that A^(2)=O . (I+A)^(100) =

    A
    100 A
    B
    `100 (I+A)`
    C
    `100 I+A`
    D
    `I+100 A`

  • Let a be a matrix of order 2xx2 such that A^(2)=O . tr (A) is equal to

    A
    `1`
    B
    `0`
    C
    `-1`
    D
    none of these

  • If A is a square matrix of order 2 xx 2 such that A^(2)=O then,

    A
    `A=((alpha,beta),(gamma,-alpha))`, where `alpha,beta,gamma` are numbes such that `alpha^(2)+betagamma=0`
    B
    `A=((alpha,beta),(beta,-alpha))` with `alpha=+-beta`
    C
    `A=((alpha,-alpha),(-beta,beta))` with `alpha^(2)+beta^(2)=1`
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    If A is a square matrix of order 3 and I is an ldentity matrix of order 3 such that A^(3) - 2A^(2) - A + 2l =0, then A is equal to

    If A is a matrix of order mxx m such that A^(2) +A + 2I = O , then

    If A is a square matrix of order 3 such that A^(2) = 2A then |A|^(2) is equal to

    Let A be a matrix of order 3xx3 such that |A|=3 . Let B=3A^(-1) and C =(adjA)/(2) , then the value of |A^(2)B^(3)C^(4)| is

    Let A be a matrix of order 3 such that A^(2)=3A-2I where, I is an identify matrix of order 3. If A^(5)=alphaa+betaI , then alphabeta is equal to

    Home
    Profile