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

Answers (1)

False

If A and B are two matrices of the same order,

then A - B = -(B - A)
For example,

\begin{aligned} &\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} -3 & -3 & -4 \\ -3 & -4 & -2 \\ -4 & -2 & -8 \end{array}\right]\\ &B-A=\left[\begin{array}{lll} 3 & 3 & 4 \\ 3 & 4 & 2 \\ 4 & 2 & 8 \end{array}\right]\\ &\Rightarrow-(B-A)=\left[\begin{array}{ccc} -3 & -3 & -4 \\ -3 & -4 & -2 \\ -4 & -2 & -8 \end{array}\right] \end{aligned}

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