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In which of the following type of matrix...

In which of the following type of matrix inverse does not exist always? a. idempotent                 b. orthogonal c. involuntary                 d. none of these

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In which of the following type of matrix there always exists an inverse? (a) Idempotent matrix (c) Involutary matrix (b) Orthogonal matrix (d) None of these

If AB=A and BA=B, then which of the following is/are true? A is idempotent b.B is is idempotent c.A^(T) is idempotent d.none of these

Knowledge Check

  • Which of the following is an orthogonal matrix ?

    A
    `[(6//7,2//7,-3//7),(2//7,3//7,6//7),(3//7,-6//7,2//7)]`
    B
    `[(6//7,2//7,3//7),(2//7,-3//7,6//7),(3//7,6//7,-2//7)]`
    C
    `[(-6//7,-2//7,-3//7),(2//7,3//7,6//7),(-3//7,6//7,2//7)]`
    D
    `[(6//7,-2//7,3//7),(2//7,2//7,-3//7),(-6//7,2//7,3//7)]`

  • Which of the following molecule does not exist in 3- D covalent solid form -

    A
    Black phosphorous
    B
    Diamond
    C
    Silicon carbide
    D
    Iodine

  • The inverse of a matrix A=[[a, b], [c, d]] is

    A
    `[[d, -b], [-c, a]]`
    B
    `[[b, -a], [d, -c]]`
    C
    `(1)/(|A|)[[1, 0], [0, 1]]`
    D
    `(1)/(ad-bc)[[d, -b], [-c, a]]`

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    Four non –zero vectors will always be a. linearly dependent b. linearly independent c. either a or b d. none of these

    A skew-symmetric matrix A satisfies the relation A^(2)+I=O, whereI is a unit matrix then A is a.idempotent b.orthogonal c.of even order d.odd order

    If A is a non-singular matrix such that AA^(T)=A^(T)A and B=A^(-1)A^(T), the matrix B is a.involuntary b.orthogonal c.idempotent d. none of these

    Which of the following is a symmetric matrix? (A) a null matrix (B) a triangular matrix (C) an idenity matrix (D) a diagonal matrix

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