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The inverse of the matrix [(1, 0,0),(a,1...

The inverse of the matrix `[(1, 0,0),(a,1,0),(b,c,1)]` is -

A

`[(1,0,0),(-a,1,0),(ac-b,-c,1)]`

B

`[(1,0,0),(-a,1,0),(-b,-c,1)]`

C

`[(1,-a,ac-b),(0,1,-c),(0,0,1)]`

D

`[(1,0,0),(-a,1,0),(ac,b,1)]`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If a,b,c, are non-zero real numbers, then the inverse of matrix A = [(a,0,0),(0,b,0),(0,0,c)] is -

    A
    `[(a^(-1),0,0),(0,b^(-1),0),(0,0,c^(-1))]`
    B
    abc`[(a^(-1),0,0),(0,b^(-1),0),(0,0,c^(-1))]`
    C
    `[(a,0,0),(0,b,0),(0,0,c)]`
    D
    `(1)/(abc)[(1,0,0),(0,1,0),(0,0,1)]`

  • If x,y,z are nonzero real number , then the inverse of matrix A= {:[( x,0,0),( 0,y,0) ,( 0,0,z) ]:} is

    A
    `{:[(x^(-1), 0,0),( 0,y^(-1) , 0),( 0,0,z^(-1))]:} `
    B
    `xyz {:[( x^(-1) ,0,0),( 0,y^(-1) ,0),( 0,0,z^(-1)) ]:}`
    C
    `(1)/(xyz) {:[( x ,0,0),( 0,y ,0),( 0,0,z) ]:}`
    D
    `(1)/(xyz) {:[( 1 ,0,0),( 0,1 ,0),( 0,0,1) ]:}`

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