A is a square matrix of order 3 with |A| = 4. Match each determinant in List I with its value in List II. | List I | List II | |---|---| | A. |adj A| | I. 32 | | B. |A^-1| | II. 16 | | C. |2A| | III. 4 | | D. |A'| | IV. 1/4 |

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

Question 61

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$A$ is a square matrix of order 3 with $|A| = 4$ . Match each determinant in List I with its value in List II.

List I	List II
A. $\|\operatorname{adj} A\|$	I. $32$
B. $\|A^{-1}\|$	II. $16$
C. $\|2A\|$	III. $4$
D. $\|A'\|$	IV. $\frac{1}{4}$

A-IV, B-II, C-I, D-IIICorrect answerYour answerA-II, B-IV, C-I, D-IIICorrect answerYour answerA-II, B-IV, C-III, D-ICorrect answerYour answerA-IV, B-II, C-III, D-ICorrect answerYour answer

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CorrectNot quiteAnswer B

Correct answer: B

$|\operatorname{adj} A| = |A|^2 = 16$ and $|A^{-1}| = \frac{1}{|A|} = \frac{1}{4}$ .
$|2A| = 2^3|A| = 32$ , and a transpose keeps the determinant: $|A'| = 4$ .

Concept: Determinants of the adjoint and the inverse
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The rule this testsThe adjoint and the inverse

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

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

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

Question 61

Explanation