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Let A and B be two square matrices of or...

Let A and B be two square matrices of order 3 and `AB = O_(3)`, where `O_(3)` denotes the null matrix of order 3. Then

A

must be `A = O_(3), B = O_(3)`

B

if `A ne O_(3)`, must be `B ne O_(3)`

C

if `A = O_(3)`, must be `B ne O_(3)`

D

may be `A ne O_(3), B ne O_(3)`

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Knowledge Check

  • Let A and B be two square matrices of order 3 and AB=O_3 , wher O_3 denotes the null matrix of order 3. Then,

    A
    must be `A=O_3,B=O_3`
    B
    If `AneO_3`,must be `BneO_3`
    C
    If `A=O_3`,must be `BneO_3`
    D
    may be `A=neO_3,B=O_3`

  • Let A be a square matrix of order 3 whose all entries are 1 and let I_3 be the identity matrix of order 3. Then the matrix A-3I_3 is

    A
    invertible
    B
    orthogonal
    C
    non-invertible
    D
    real skew symmetric matrix

  • Let A be a square matrix of order 3xx3 , then |KA| is equal to

    A
    K|A|
    B
    `K^2|A|`
    C
    `K^3|A|`
    D
    3K|A|

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