List of practice Questions

The determinant of a \(4 \times 4\) matrix \(A\) is 3. The value of the determinant of \(2A\) is ____________.

Let \( n > 1 \). Consider an \( n \times n \) matrix \( M \) with its elements from \( \mathbb{R} \). Let the vector \( (0, 1, 0, 0, \ldots, 0) \in \mathbb{R}^n \) be in the null space of \( M \). Which of the following options is/are always correct?