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
Let matrix $\mathrm{B}$ be the adjoint of a square matrix $\mathrm{A}, \ell$ be the identitymatrix of same order as A. If $k(\neq 0)$ is the determinant of the matrix $\mathrm{A}$, then what is $\mathrm{AB}$ equal to?
MathematicsDeterminantsNDANDA 2018 (Phase 2)
Options:
  • A $\ell$
  • B $\mathrm{k} \ell$
  • C $\mathrm{k}^{2} \ell$
  • D $(1 / k) \ell$
Solution:
2482 Upvotes Verified Answer
The correct answer is: $\mathrm{k} \ell$
$\mathrm{B}=\mathrm{adj} \mathrm{A}, \mathrm{I}=$ Identity matrix, $|\mathrm{A}|=k$
$\mathrm{AB}=\mathrm{A}(\operatorname{adj} \mathrm{A})=|\mathrm{A}| \mathrm{I}=k \mathrm{I}$

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.