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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Matrices

NDA 2023 · Mathematics · Matrices

Consider the following statements in respect of square matrices A,...

Consider the following statements in respect of square matrices A,B,CA, B, C each of same order nn : 1. AB=AC⇒B=CA B=A C \Rightarrow B=C if AA is non-singular 2. If BX=CXB X=C X for every column matrix X having n rows then B=CB=C Which of the statement given above is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

A B=A CIfAIf A is non singular hence A^{-1}exist.A−1AB=A−1AC∴B=Cexist. A^{-1} A B=A^{-1} A C\therefore \quad B=C but BX=CX⇒B=CB X=C X \Rightarrow B=C is not necessarily true. e.g. \left[1234\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]\left[\begin{array}{l}0 \\ 0\end{array}$\right]=\left[\begin{array}{ll}2 & 3 \\ 7 & 5\end{array}$\right]\left[\begin{array}{l}0 \\ 0\end{array}$\right].
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