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The number of $3 \times 3$ matrices $A$ whose entries are either $0 o r 1$ and for which the system $A [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}]$ has exactly two distinct solutions, is

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Correct option is A

Since, Axyz=100 is linear equation in three variables and that could have only unique, no solution or infinitely many solutions.∴ It is the possible to have two solutionsHence, number of matrices A is zero.

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The number of 3×3 matrices A whose entries are either 0 or 1 and for which the system Axyz=100 has exactly two distinct solutions, is

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The number of $3 \times 3$ matrices $A$ whose entries are either $0 o r 1$ and for which the system $A [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}]$ has exactly two distinct solutions, is