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please solve rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice questions  question 6 maths textbook solution

Answers (1)

option (a) AB is non-singular

Given: A & B are non-singular matrix

Hint: A & B are singular matrices only when the\left | A \right |\& \left | B \right | is equal to Zero

Solution:

If A & B are non-singular matrices of order nxn


\begin{aligned} &\therefore|\mathrm{A}| \neq 0 \text { and }|\mathrm{B}| \neq 0 \\ &|\mathrm{AB}|=|\mathrm{A}||\mathrm{B}| \\ &\Rightarrow \therefore|\mathrm{AB}| \neq 0 \end{aligned}

∴  AB is non-singular

Hence option (a) is correct.

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