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TS EAMCET · Maths · Matrices

\[
\text { If } A=\left[\left.\begin{array}{lll}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{array} \right\rvert\, \text {, then }\left(A A^{\prime}\right)^{\prime}=\right.
\]

  1. A \[
    \left[\begin{array}{ccc}
    14 & 32 & 50 \\
    32 & 122 & 194 \\
    50 & 194 & 256
    \end{array}\right]
    \]
  2. B \[
    \text { }\left[\begin{array}{ccc}
    14 & 50 & 32 \\
    32 & 122 & 194 \\
    50 & 194 & 122
    \end{array}\right]
    \]
  3. C \[
    \left[\begin{array}{ccc}
    14 & 32 & 50 \\
    32 & 194 & 122 \\
    32 & 122 & 77
    \end{array}\right]
    \]
  4. D \[
    \left[\begin{array}{ccc}
    14 & 32 & 50 \\
    32 & 77 & 122 \\
    50 & 122 & 194
    \end{array}\right]
    \]
Verified Solution

Answer & Solution

Correct Answer

(D) \[
\left[\begin{array}{ccc}
14 & 32 & 50 \\
32 & 77 & 122 \\
50 & 122 & 194
\end{array}\right]
\]

Step-by-step Solution

Detailed explanation

We have, \[ A=\left[\begin{array}{lll} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right] \Rightarrow A^{\prime}=\left[\begin{array}{lll} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array}\right] \] Now,…