Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If A is a matrix of order 3, and |adj A| = 36, then which of the following statements is true for |A|?

Options:

|A| can be 6.

|A| can be -6.

|A| can be both 6 and -6.

|A| can never be negative.

Correct Answer:

|A| can be both 6 and -6.

Explanation:

|adj A| = \( { |A| }^{ n-1 } \), where n is the order of the matrix

|adj A| = \( { |A| }^{ 3-1 } \)

36 = \( { |A| }^{ 2 } \)

|A| =6 or -6