Which of the following statements are true?
I. $(A')' = A$ .
II. $(kA)' = kA'$ for any number $k$ .
III. $(AB)' = A'B'$ whenever $AB$ is defined.
IV. $(A + B)' = A' + B'$ for matrices of the same order.

All four: I, II, III and IVCorrect answerYour answerI, II and IV onlyCorrect answerYour answerI, II and III onlyCorrect answerYour answerI and IV onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Transposing twice gives back $A$ , a number passes through the transpose, and so does a sum: I, II and IV are true.
The product law reverses the order: $(AB)' = B'A'$ , so III is false.

Concept: Properties of the transpose
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsThe transpose

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