Doubt from Matrices

The total number of matrices
A= \begin{bmatrix}0 & 2y & 1\\2x & y & -1\\2x & -y & 1\end{bmatrix}, (x,y\in R,x\ne y) for which A^TA=3I_3 is

[JEE Main 2019 | 9th April II]

( A ) 2
( B ) 4
( C ) 3
( D ) 6

Answer: ( B )

Using the given condition multiply the AA’ and equate it to 3I ,now from that you will get value of x and y but there will be 2 values each for x and y …so basically we need to find the no of ordered pairs ,which is 4,to determine the no of matrices

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Yeah, got it. thanks! I initially made a stupid mistake. That’s why I didn’t get it.

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You’ll get two values of x and y. So 4 possible matrices.