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Let \( \alpha, \beta \) and \( \gamma \) be real numbers. Consider the following system of linear equations
\( x + 2y + z = 7 \)
\( x + \alpha z = 11 \)
\( 2x - 3y + \beta z = \gamma \)
Match each entry in List-I to the correct entries in List-II.

The correct option is:

Let \( M=(a_{ij}),\, i,j\in\{1,2,3\} \), be the \( 3\times3 \) matrix such that \( a_{ij}=1 \) if \( j+1 \) is divisible by \( i \), otherwise \( a_{ij}=0 \). Then which of the following statements is(are) true?

Then the number of invertible matrices in \( R \) is:

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JEE Advanced 2023 Paper - 2

Then the number of invertible matrices in \( R \) is: