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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Matrices

NDA 2018 · Mathematics · Matrices

Let matrix B be the adjoint of a square matrix A,I be the identity...

Let matrix B be the adjoint of a square matrix A,I be the identity matrix of same order as AA. If k(≠0)k(\neq 0) is the determinant of the matrix A , then what is AB equal to?

Options

  1. AI
  2. BkI
  3. Ck2I\mathrm{k}^2 \mathrm{I}
  4. D(1/k)I(1 / k) I

Correct answer

B. kI

Step-by-step solution

B=adj⁡A,I=Identity matrix, ∣A∣=kAB=A(adj⁡A)=∣A∣I=kI.\begin{aligned} & \mathrm{B}=\operatorname{adj} \mathrm{A}, \mathrm{I}=\mathrm{Identity} \text{ matrix, }|\mathrm{A}|=k \\ & \mathrm{AB}=\mathrm{A}(\operatorname{adj} \mathrm{A})=|\mathrm{A}| \mathrm{I}=k \mathrm{I}.\end{aligned}
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