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

This is a fundamental property of determinants. If a matrix has two identical rows or two identical columns, its determinant is zero. This can be understood by considering that swapping two rows negates the determinant. If the two rows are identical, swapping them changes nothing about the matrix, but the determinant must be negated. The only number that is equal to its own negative is zero. Therefore, the value of the determinant is 0.