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AP EAMCET · Maths · Matrices

\(A=\left[\begin{array}{lll}0 & 1 & 2 \\ 2 & 3 & 0 \\ 4 & 0 & 3\end{array}\right]\) and \(B\) is a matrix such that \(A B=B A\). If
\(A B\) is not an identity matrix, then the matrix that can be taken as B is

  1. A \(\left[\begin{array}{ccc}-9 & -3 & 6 \\ -6 & 8 & -4 \\ 12 & -4 & -2\end{array}\right]\)
  2. B \(\left[\begin{array}{ccc}9 & -3 & 6 \\ -6 & 8 & -4 \\ -12 & -4 & 2\end{array}\right]\)
  3. C \(\left[\begin{array}{ccc}9 & -3 & -6 \\ -6 & 8 & -4 \\ -12 & 4 & -2\end{array}\right]\)
  4. D \(\left[\begin{array}{ccc}9 & -3 & -6 \\ -6 & -8 & 4 \\ -12 & 4 & -2\end{array}\right]\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\left[\begin{array}{ccc}9 & -3 & -6 \\ -6 & -8 & 4 \\ -12 & 4 & -2\end{array}\right]\)

Step-by-step Solution

Detailed explanation

\(\mathrm{A}=\left[\begin{array}{lll} 0 & 1 & 2 \\ 2 & 3 & 0 \\ 4 & 0 & 3 \end{array}\right] \text { and let } \mathrm{B}=\left[\begin{array}{ccc} x & y & z \\ a & b & c \\ u & v & w \end{array}\right]\) Now \(\mathrm{AB}=\mathrm{BA}\)…