Which of the following statements are true?
I. $(AB)C = A(BC)$ whenever the products are defined.
II. $A(B + C) = AB + AC$ whenever the products are defined.
III. $AB = BA$ for any two square matrices of the same order.
IV. $AI = IA = A$ for a square matrix $A$ and the identity matrix of its order.

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

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Multiplication is associative (I), distributes over addition (II), and $I$ leaves a matrix unchanged from either side (IV).
It is not commutative: for $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 0 \\ 1 & 3 \end{bmatrix}$ , $AB \ne BA$ . So III is false.

Concept: Properties of matrix multiplication
Typical timeTypical: 120 s
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The rule this testsProperties of multiplication, and powers

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