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  • please solve rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice questions question 2 maths textbook solution

please solve rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice questions  question 2 maths textbook solution

 

Answers (1)

(c) BA = CA

Given: A is an invertible matrix of order 3

Hints: A inverse is possible only when \left | A \right |\neq 0

Solution:

\left | adj A \right | = \left | A \right |^{2}                                                   \left [ \therefore \left | adj A \right | = \left | A \right |^{n-1} \right ]

∴ Option A is correct

Now option B,

We know that in of invertible matrix

\left ( A^{-1} \right )^{-1}=A

∴ Option B is also correct

Now option D    

\left ( AB \right )=B^{-1}A^{-1}                                            (∴  A & B two invertible matrices of the same order)

Now, option C

B A = C A

⇒B=C

But it is given B ≠ C. Hence Option C is not true.

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