Question

The determinant of a matrix is always positive.

• A. True
• B. False

Answer 1

The correct option is B

False

The determinant value of a matrix can be positive or negative. While explaining the determinant we discussed that determinant is a unique value associated to the matrix. This unique value may be either positive or negative. We discussed about the area of the parallelogram formed by 2 vectors in x-y plane which is given by the determinant of the matrix of the 2 vectors. Now this determinant may come out to be negative despite the fact that area cannot be negative. The negative sign here will indicate the direction of the area vector and nothing else. Also it’s just the way the numbers are arranged in the matrix which decides the sign of the determinant value.