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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 A + B = B + A.

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

Answers (1)

True

If A and B are two square matrices of the same order, then A + B = B + A ( Property of square matrix)

For example,

\begin{array}{l} \text {Let } A=\left[\begin{array}{lll} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 4 & 1 \end{array}\right] \text { and } B=\left[\begin{array}{lll} 4 & 5 & 7 \\ 5 & 5 & 6 \\ 7 & 6 & 9 \end{array}\right] \\ A+B=\left[\begin{array}{lll} 5 & 7 & 10 \\ 7 & 6 & 10 \\ 10 & 10 & 10 \end{array}\right] \\ \Rightarrow \quad B+A=\left[\begin{array}{lll} 5 & 7 & 10 \\ 7 & 6 & 10 \\ 10 & 10 & 10 \end{array}\right] \\ \end{array}

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