Question

The number of `3xx3` matrices `A` whose entries are either `0or1` and for which the system `A[x y z]=[1 0 0]` has exactly two distinct solution is a. 0 b. `2^9-1` c. `168` d. `2`

Answer 1

Correct Answer - A
Since, `A[(x), (y), (z)] = [(1), (0), (0)]` is linear equation in three variables and that could have only unique, no solution or infinitely many solution.
`therefore` It is not possible to have two solutions.
Hence, number of matrices A is zero.