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If x, y, z are non-zero real numbers, th...

If x, y, z are non-zero real numbers, 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)
`:." "A=[{:(x,0,0),(0,y,0),(0,0,z):}]`
`rArr" "|A|=[{:(x,0,0),(0,y,0),(0,0,z):}]=xyzne0`
`A_(11)=yz, A_(12)=0, A_(13)=0`
`A_(21)=0, A_(22)=zx, A_(23)=0`
`A_(31)=0, A_(32)=0, A_(32)=0, A_(33)=xy`
`:." adj A"=[{:(yz,0,0),(0,zx,0),(0,0,xy):}]=[{:(yz,0,0),(0,zx,0),(0,0,xy):}]`
`"and A"^(-1)=1/|A|".adj A"=1/(xyz)[{:(yz,0,0),(0,zx,0),(0,0,xy):}]`
`=[{:(1/x,0,0),(0,1/y,0),(0,0,1/z):}]`
`=[{:(x^(-1),0,0),(0,y^(-1),0),(0,0,z^(-1)):}]`
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