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GUJCET · Maths · Matrices
If \(A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\), and \(B=\) ____________ then, \(A B=B A(\because B \neq I)\)
- A \(\left[\begin{array}{ll}x & y \\ 0 & x\end{array}\right]\)
- B \(\left[\begin{array}{ll}x & y \\ 0 & y\end{array}\right]\)
- C \(\left[\begin{array}{ll}x & x \\ y & 0\end{array}\right]\)
- D \(\left[\begin{array}{ll}x & 0 \\ y & y\end{array}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[\begin{array}{ll}x & y \\ 0 & x\end{array}\right]\)
Step-by-step Solution
Detailed explanation
\(A B = \left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right] \left[\begin{array}{ll}x & y \\ z & w\end{array}\right] = \left[\begin{array}{ll}x+z & y+w \\ z & w\end{array}\right]\) \(B A = \left[\begin{array}{ll}x & y \\ z & w\end{array}\right] \left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right] = \left[\begin{array}{ll}x & x+y \\ z & z+w\end{array}\right]\)
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