Question

If any two rows (or columns) of a determinant are identical then the value of the determinant is:

• A. 1
• B. 0
• C. \(\infty\)
• D. unchanged

Hint:

Memorizing the basic properties of determinants is essential for linear algebra. The key properties include: det(A\(^T\))=det(A), det(AB)=det(A)det(B), and the effect of row/column operations (swapping, scaling, adding a multiple of another row/column).

Answer 1

The Correct Option is B

A fundamental property of determinants states that if a matrix possesses two identical rows or two identical columns, its determinant is zero. This is because swapping two rows negates the determinant. If two rows are identical, swapping them results in no change to the matrix, yet the determinant must be negated. The sole number equal to its own negative is zero, thus the determinant's value is 0.