Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If $A=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]$ then $A^5=$
MathematicsMatricesJEE Main
Options:
  • A $5 A$
  • B $10 \mathrm{~A}$
  • C $16 \mathrm{~A}$
  • D $32 A$
Solution:
1991 Upvotes Verified Answer
The correct answer is: $16 \mathrm{~A}$
$A=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]$ $\Rightarrow A^5=\left[\begin{array}{ccc}2^5 & 0 & 0 \\ 0 & 2^5 & 0 \\ 0 & 0 & 2^5\end{array}\right]=$ $=2^4\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]$
$=16 \mathrm{~A}$

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.