Which of the following statements are true?
I. $A + B = B + A$ for matrices $A$ and $B$ of the same order.
II. $A - B = B - A$ for matrices $A$ and $B$ of the same order.
III. $k(A + B) = kA + kB$ for any number $k$ .
IV. $(k + l)A = kA + lA$ for any numbers $k$ and $l$ .

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

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Addition is done element by element, so it is commutative like the addition of numbers (I), and a number multiplies out over a sum either way (III and IV).
$B - A = -(A - B)$ , so II holds only when $A = B$ .

Concept: Properties of addition and scalar multiplication
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsAddition and multiplication by a scalar

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