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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Matrices

NDA 2017 · Mathematics · Matrices

If A=( array cc -2 & 2 2 & -2 array ) , then which one of the...

If A=\left(−222−2\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right), then which one of the following is correct?

Options

  1. AA2=−2A\mathrm{A}^2=-2 \mathrm{ A}
  2. BA2=−4A\mathrm{A}^2=-4 \mathrm{ A}
  3. CA2=−3A\mathrm{A}^2=-3 \mathrm{ A}
  4. DA2=4A\mathrm{A}^2=4 \mathrm{ A}

Correct answer

B. A2=−4A\mathrm{A}^2=-4 \mathrm{ A}

Step-by-step solution

A=(−222−2)A2=(−222−2)(−222−2)\begin{aligned} & A=\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right) \\ & A^2=\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right)\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right)\end{aligned}=(4+4−4−4−4−44+4)=(8−8−88)=−4(−222−2)=−4A\begin{aligned} & =\left(\begin{array}{cc}4+4 & -4-4 \\ -4-4 & 4+4\end{array}\right)=\left(\begin{array}{cc}8 & -8 \\ -8 & 8\end{array}\right) \\ & =-4\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right)=-4 \mathrm{ A}\end{aligned}
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