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GUJCET · Maths · Matrices

If \(A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\), and \(B=\) ____________ then, \(A B=B A(\because B \neq I)\)

  1. A \(\left[\begin{array}{ll}x & y \\ 0 & x\end{array}\right]\)
  2. B \(\left[\begin{array}{ll}x & y \\ 0 & y\end{array}\right]\)
  3. C \(\left[\begin{array}{ll}x & x \\ y & 0\end{array}\right]\)
  4. D \(\left[\begin{array}{ll}x & 0 \\ y & y\end{array}\right]\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\left[\begin{array}{ll}x & y \\ 0 & x\end{array}\right]\)

Step-by-step Solution

Detailed explanation

\(A B = \left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right] \left[\begin{array}{ll}x & y \\ z & w\end{array}\right] = \left[\begin{array}{ll}x+z & y+w \\ z & w\end{array}\right]\) \(B A = \left[\begin{array}{ll}x & y \\ z & w\end{array}\right] \left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right] = \left[\begin{array}{ll}x & x+y \\ z & z+w\end{array}\right]\)