If x, y & z are non zero real numbers, the inverse of matrix A = \left[\begin{array}{ccc}x & 0 & 0 \ \text{ 0} & y & 0 \ \text{ 0} & 0 & z \ ]\end{array} is:

Correct Answer is : [x−100 0y−10 00z−1]

\left[\begin{array}{c}x^{−1\end{array} , 0 , 0 ; \text{ 0} , y^{−1} , 0 ; \text{ 0} , 0 , z^{−1} ; ]}

xyz\left[\begin{array}{c}x^{−1\end{array} , 0 , 0 ; \text{ 0} , y^{−1} , 0 ; \text{ 0} , 0 , z^{−1} ; ]}

\frac{1}{xyz}\left[\begin{array}{c}x^{−1\end{array} , 0 , 0 ; \text{ 0} , y^{−1} , 0 ; \text{ 0} , 0 , z^{−1} ; ]}

\frac{1}{xyz}\left[\begin{array}{ccc}1 & 0 & 0 \ \text{ 0} & 1 & 0 \ \text{ 0} & 0 & 1 \ ]\end{array}

CUET UG Math 19 Jun 2023 Paper

Question : 21 of 50

Marks: +1, -0

If x, y & z are non zero real numbers, the inverse of matrix A =

{[\table x , 0 , 0 ; \text" 0" , y , 0 ; \text" 0" , 0 , z ; ]}

is:

${[\table x^{−1} , 0 , 0 ; \text" 0" , y^{−1} , 0 ; \text" 0" , 0 , z^{−1} ; ]}$
$xyz{[\table x^{−1} , 0 , 0 ; \text" 0" , y^{−1} , 0 ; \text" 0" , 0 , z^{−1} ; ]}$
$\;{1}/{xyz}{[\table x^{−1} , 0 , 0 ; \text" 0" , y^{−1} , 0 ; \text" 0" , 0 , z^{−1} ; ]}$
$\;{1}/{xyz}{[\table 1 , 0 , 0 ; \text" 0" , 1 , 0 ; \text" 0" , 0 , 1 ; ]}$

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