Search any question & find its solution
Question:
Answered & Verified by Expert
If \(A=\left[\begin{array}{lll}2 & 0 & 0 \\ 2 & 2 & 0 \\ 2 & 2 & 2\end{array}\right]\), then \(\operatorname{adj}(\operatorname{adj} A)\) is equal to -
Options:
Solution:
1340 Upvotes
Verified Answer
The correct answer is:
\(16\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]\)
\(|A|=\left[\begin{array}{lll}
2 & 0 & 0 \\
2 & 2 & 0 \\
2 & 2 & 2
\end{array}\right]=(2)(2)(2)=8\)
Now adj \((\operatorname{adj} A)=|\mathrm{A}|^{3-2} \mathrm{~A}\)
\(=8\left[\begin{array}{lll}
2 & 0 & 0 \\
2 & 2 & 0 \\
2 & 2 & 2
\end{array}\right]=16\left[\begin{array}{ccc}
1 & 0 & 0 \\
1 & 1 & 0 \\
1 & 1 & 1
\end{array}\right]\)
2 & 0 & 0 \\
2 & 2 & 0 \\
2 & 2 & 2
\end{array}\right]=(2)(2)(2)=8\)
Now adj \((\operatorname{adj} A)=|\mathrm{A}|^{3-2} \mathrm{~A}\)
\(=8\left[\begin{array}{lll}
2 & 0 & 0 \\
2 & 2 & 0 \\
2 & 2 & 2
\end{array}\right]=16\left[\begin{array}{ccc}
1 & 0 & 0 \\
1 & 1 & 0 \\
1 & 1 & 1
\end{array}\right]\)
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.