Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

Let A be a square matrix of order n.

Statement-1: $|adj (adj\, A)|=|A|^{(n-1)^2}$

Statement-2: $adj (adj\, A) =|A|^{n-2} A$

Options:

Statement-1 is True, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1. 

Statement-1 is True, Statement-2 is False.

Statement-1 is False, Statement-2 is True.

Correct Answer:

Statement-1 is True, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Explanation:

Statement-1 is true

$∴|adj (adj\, A)|=||A|^{n-2}A|=|A|^{(n-2)n}|A|$

$⇒|adj (adj\, A)|=|A|^{n^2-2n+1}=|A|^{(n-1)^2}$