GATE 2015 CS (CS2) – Question 57
For $M=\begin{pmatrix}3&4&45\\7&9&105\\13&2&195\end{pmatrix}$, add the third row to the second, then subtract the third column from the first. Find the resulting determinant.
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Correct answer: 0
Explanation
Initially the third column is fifteen times the first, so the determinant is zero. Adding one row to another preserves the determinant. Subtracting one column from another also preserves it. Therefore the resulting determinant remains zero; no full expansion is needed.