Which of the following statements are true?
I. $|A'| = |A|$ for every square matrix $A$ .
II. $|3A| = 3|A|$ for every square matrix $A$ of order 3.
III. A determinant with a row of zeros has the value 0.
IV. Interchanging two rows of a determinant leaves its value unchanged.

I and III onlyCorrect answerYour answerI, II and III onlyCorrect answerYour answerI, III and IV onlyCorrect answerYour answerIII onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Expanding along a row of $A$ is expanding along a column of $A'$ , so I is true; expanding along the zero row makes every term 0, so III is true.
$|3A| = 3^3|A| = 27|A|$ , so II is false; swapping two rows changes the sign, so IV is false.

Concept: Facts about determinants
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsThe determinant of a matrix

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

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