10
QuizMultiple Choice

Matrices and Their Inverses — Quiz

Question 10 • Advanced Algebra: Concepts and Connections

Which statement is true about the determinant of a matrix?

Answer
A
The determinant of an inverse matrix is equal to zero.
B
The determinant of an identity matrix is equal to zero.
C
The determinant of a zero matrix is equal to one.
D
The determinant of a singular matrix is equal to zero.

Explanation

A singular matrix is not invertible, which happens exactly when its determinant is zero. So the true statement is “The determinant of a singular matrix is equal to zero.” An inverse matrix has a nonzero determinant, while the determinant of a zero matrix is 0 and the determinant of an identity matrix is 1.

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