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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Matrices

NDA 2011 · Mathematics · Matrices

If A=[ array ll α & 0 1 & 1 array ] and B=[ array ll 1 & 0 2 & 1...

If A=\left[α011\begin{array}{ll}\alpha & 0 \\ 1 & 1\end{array}\right] and B=\left[1021\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right] such that A2=BA^2=B, then what is the value of α\alpha ?

Options

  1. A-1
  2. B1
  3. C2
  4. D4

Correct answer

B. 1

Step-by-step solution

A=\left[α011\begin{array}{ll}\alpha & 0 \\ 1 & 1\end{array}\right] \begin{array}{ll}\therefore & \mathrm{A}^2=\left[\begin{array}{ll}\alpha & 0 \\ 1 & 1\end{array}\right] \times\left[α011\begin{array}{ll}\alpha & 0 \\ 1 & 1\end{array}\right] \\ \Rightarrow & \mathrm{A}^2=\left[α20α+11\begin{array}{cc}\alpha^2 & 0 \\ \alpha+1 & 1\end{array}\right]\end{array}GivenGiven\mathrm{A}^2=\mathrm{I}\therefore\left[α20α+11\begin{array}{cc}\alpha^2 & 0 \\ \alpha+1 & 1\end{array}\right]=\left[1021\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right]⇒α+1=2⇒α=1.\begin{array}{rrr}\Rightarrow & \alpha+1=2 \\ \Rightarrow & \alpha=1 .\end{array}$
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