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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Matrices

NDA 2015 · Mathematics · Matrices

If A=[ array ccc 1 & 1 & -1 2 & -3 & 4 3 & -2 & 3 array ] and B=[...

If A=\left[11−12−343−23\begin{array}{ccc}1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3\end{array}\right] and B=\left[−1−2−161265105\begin{array}{ccc}-1 & -2 & -1 \\ 6 & 12 & 6 \\ 5 & 10 & 5\end{array}\right] then which of the following is/are correct? 1. AA and BB commute. 2. ABA B is a null matrix. Select the correct answer using the code given below:

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

B. 2 only

Step-by-step solution

A=[11−12−343−23];B=[−1−2−161265105]AB=[000000000]BA=[−87−1048−426040−3550]as AB≠BASo A and B are not commute. \begin{aligned} & \mathrm{A}=\left[\begin{array}{ccc}1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3\end{array}\right] ; \mathrm{B}=\left[\begin{array}{ccc}-1 & -2 & -1 \\ 6 & 12 & 6 \\ 5 & 10 & 5\end{array}\right] \\ & \mathrm{AB}=\left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right] \\ & \mathrm{BA}=\left[\begin{array}{ccc}-8 & 7 & -10 \\ 48 & -42 & 60 \\ 40 & -35 & 50\end{array}\right] \\ & \text{as } \mathrm{AB} \neq \mathrm{BA} \\ & \text{So } \mathrm{A} \text{ and } \mathrm{B} \text{ are not commute. }\end{aligned}
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