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Let A be a 2xx2 invertible matrix . For ...

Let A be a `2xx2` invertible matrix . For which of the following functions det (f(A)) = f (det (A)) is not true ?

A

f(x) `= x^(3)`

B

f(x)`=x^(-1), x ne 0`

C

f(x) = 1 +x

D

f(x) `=x^(-3) , x ne 0`

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • Let A be an invertible matrix, then which of the following is not true?

    A
    `A^(-1)=|A|^(-1)`
    B
    `(A^(2))^(-1)=(A^(-1))^(2)`
    C
    `(A')^(-1)=(A^(-1))`
    D
    None of these

  • Let A and B be two invertible matrices of order 3xx3 . If det. (ABA^(T)) = 8 and det. (AB^(-1)) = 8, then det. (BA^(-1)B^(T)) is equal to

    A
    16
    B
    `(1)/(16)`
    C
    `(1)/(4)`
    D
    1

  • If A is an invertible matrix of order 2, then det (A^(-1)) is equal to

    A
    det(A)
    B
    `(1)/(det(A))`
    C
    1
    D
    0

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