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If A is square matrix such that A^(2)=A,...

If A is square matrix such that `A^(2)=A`, then show that `(I+A)^(3)=7A+I`.

A

A

B

I

C

I-A

D

3A

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • If A is a square matrix such that A^(2)=A, then (I+A)^(3)-7A is equal to___

    A
    A
    B
    I-A
    C
    I
    D
    3A

  • A is a square matrix such that A^(3)=I , then A^(-1) is equal to -

    A
    `A^(2)`
    B
    A
    C
    `A^(3)`
    D
    none of these

  • If A be a square matrix then A^(2) will be

    A
    symmetric matrix
    B
    skew-symmetric matrix
    C
    diagonal matrix
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    If A is a square matrix such that A^(2)= I , then (A-I)^(3)+(A+I)^(3)-7A is equal to

    If A is a square matrix such that A^2=A , then write the value of 7A-(I+A)^3, where I is the identity matrix.

    If A is a 2xx2 matrix such that A^(2)-4A+3I=O , then prove that (A+3I)^(-1)=7/24 I-1/24 A .

    If A is square matric and A^2=A,(I+A)^3-7A will be

    If A is a matrix of order n such that A^(T)A=I and X is any matrix such that X=(A+I)^(-1) (A-I) , then show that X is skew symmetric matrix.

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