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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Matrices

NDA 2022 · Mathematics · Matrices

If A is the identity matrix of order 3 and B is its transpose, then...

If AA is the identity matrix of order 3 and BB is its transpose, then what is the value of the determinant of the matrix C=A+BC=A+B ?

Options

  1. A1
  2. B2
  3. C4
  4. D8

Correct answer

D. 8

Step-by-step solution

 Given that A=Iand B=AT=IT=INow C=A+B=I+I=2I∴∣C∣=(2)3∣I∣=8.1=8\begin{aligned} & \text{ Given that } A=I \\ & \text{and } B=A^T=I^T=\mathrm{I} \\ & \text{Now } \mathrm{C}=\mathrm{A}+\mathrm{B}=\mathrm{I}+\mathrm{I}=2 \mathrm{I} \\ & \therefore \quad|C|=(2)^3|I|=8.1=8\end{aligned}
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