Perform the following operations on the matrix

⎡ 3  4   45⎤
⎢ 7  8  105⎥
⎣13  2  195⎦ 

1. Add the third row to the second row.
2. Subtract the third column from the first column.

The determinant of the resultant matrix is _____________.
(A) 0
(B) 1
(C) 50
(D) 100


Answer: (A)

Explanation: The given matrix is singular matrix as its last column is a multiple of first column. If we multiply 15 with first column, we get the third column.
Ranks is less than 3, determinant must be 0.


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