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If x,y,z are nonzero real number , then ...

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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The correct Answer is:
A
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