A is a square matrix of order 3 with |A| = 4. What is |adj A|?

Determinants, Adjoint & Inverse · Question 54 of 87

Question 54

MediumOriginal question

$A$ is a square matrix of order 3 with $|A| = 4$ . What is $|\operatorname{adj} A|$ ?

4

Correct answerYour answer

12

Correct answerYour answer

16

Correct answerYour answer

64

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$A(\operatorname{adj} A) = |A|I$ ; taking determinants, $|A||\operatorname{adj} A| = |A|^3$ .
So $|\operatorname{adj} A| = |A|^{3 - 1} = 4^2 = 16$ .

Worth noting

64 is $|A|^3$ , the determinant of $|A|I$ , before dividing by $|A|$ .

Ten questions from Determinants, Adjoint & Inverse, at your own pace.

Ten questions from Determinants, Adjoint & Inverse, at your own pace.