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Let M be a 2 x 2 symmetric matrix with i...

Let M be a 2 x 2 symmetric matrix with integer entries. Then M is invertible if (a)The first column of M is the transpose of the second row of M (b)The second row of Mis the transpose of the first olumn of M (c) M is a diagonal matrix with non-zero entries in the main diagonal (d)The product of entries in the main diagonal of Mis not the square of an integer

A

the first column of M is the transpose of the second row of M.

B

the second row of M is the transpose of the first column of M.

C

M is a diagonal matrix with non-zero entries in the main diagonal.

D

the product of entries in the main diagonal of M is not the square of an integer.

Text Solution

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The correct Answer is:
C, D
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Knowledge Check

  • If A^(T) is the transpose of a square matrix A then A is called a skew-symmetrix matrix if it is___

    A
    `A^(T)=-A`
    B
    `"AA"^(T)=A`
    C
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    D
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  • If M is any square matrix of order 3 over R and if M' be the transpose of M, then adj(M')-(adjM)' is equal to

    A
    M
    B
    M'
    C
    null matrix
    D
    indentity matrix

  • If a square matrix A is equal to its transpose A^(T) , then A is called a___

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

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