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For a 3xx 3 matrix A, if A .(adj A)=[[3,...

For a `3xx 3` matrix A, if `A .(adj A)=[[3,0,0],[0,3,0[,[0,0,3]]` then `|A|=`

A

a.9

B

b.3

C

c.27

D

d.0

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • For any 2xx 2 matrix A, if A . adj A = [[7,0],[0,7]] then |A| is equal to

    A
    7
    B
    14
    C
    49
    D
    0

  • For a 3xx 3 matrix A, if det A=3 , then det (adj A)=

    A
    -3
    B
    3
    C
    9
    D
    27

  • The inverse of the matrix A = [[2,0,0],[0,3,0],[0,0,4]] is

    A
    `(1)/(24)[[2,0,0],[0,3,0],[0,0,4]]`
    B
    `[[2,0,0],[0,3,0],[0,0,4]]`
    C
    `(1)/(24)[[1,0,0],[0,1,0],[0,0,1]]`
    D
    `[[(1)/(2),0,0],[0,(1)/(3),0],[0,0,(1)/(4)]]`

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