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  • Which of the following statements are True or False If A and B are two square matrices of the same order, then AB = BA.

Which of the following statements are True or False
If A and B are two square matrices of the same order, then AB = BA.

 

Answers (1)

False

Matrix multiplication is not commutative.
For example,

\begin{array}{l} \text { Let } A=\left[\begin{array}{ll} 1 & 3 \\ 3 & 2 \end{array}\right] \\ B=\left[\begin{array}{ll} 1 & 2 \\ 2 & 1 \end{array}\right] \\ \Rightarrow A B=\left[\begin{array}{ll} 7 & 5 \\ 7 & 8 \end{array}\right] \text { and } B A=\left[\begin{array}{ll} 7 & 7 \\ 5 & 8 \end{array}\right] \\ \Rightarrow A B \neq B A \end{array}

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