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If a, b, c and are real numbers and A =[...

If a, b, c and are real numbers and A `=[{:( a,b),(c,d) :}]` prove that ` A^(2) -(a+d) A+(ad-bc) I=0`

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If A=[(a,b),(c,d)] , where a, b, c and d are real numbers, then prove that A^(2)-(a+d)A+(ad-bc) I=O . Hence or therwise, prove that if A^(3)=O then A^(2)=O

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Knowledge Check

  • If a, b, c, d and p are distinct real numbers such that (a^(2) + b^(2) + c^(2)) p^(2) - 2(ab + bc + cd) p + (b^(2) + c^(2) + d^(2)) le 0 , then a, b, c, d are in

    A
    A.P.
    B
    G.P.
    C
    H.P.
    D
    ab = cd

  • if a,b, c, d and p are distinct real number such that (a^(2) + b^(2) + c^(2))p^(2) - 2p (ab + bc + cd) + (b^(2) + c^(2) + d^(2)) lt 0 then a, b, c, d are in

    A
    A.P.
    B
    G.P.
    C
    H.P.
    D
    None of these

  • If {:A=[(a,b),(c,d)]:} such that ad - bc ne 0 , then A^(-1) , is

    A
    `1/(ad-bc){:[(a,-b),(-c,a)]:}`
    B
    `1/(ad-bc){:[(a,-b),(-c,a)]:}`
    C
    `{:[(d,b),(-c,a)]:}`
    D
    none of these

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    If a, b, c, d are positive numbers in HP then prove that ad gt bc .

    Statement 1: if a ,b ,c ,d are real numbers and A=[a b c d]a n dA^3=O ,t h e nA^2=Odot Statement 2: For matrix A=[a b c d] we have A^2=(a+d)A+(a d-b c)I=Odot

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    If A=[(a,b),(c,d)] such that ad-bc!=0 , then A^(-1) is equal to

    If a, b, c and d are four positive real numbers such that sum of a, b and c is even the sum of b,c and d is odd, then a^2-d^2 is necessarily

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