Question

Assertion :The inverse of a matrix $A=\left[\begin{array}{ccc}43& 1& 6\\ 35& 7& 4\\ 17& 3& 2\end{array}\right]$ does not exist. Reason: The inverse ofsingular matrix is not possible.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A),
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A)is true but (R} is false,
• D. (A)is false but (R} is true.

Answer 1

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A),

$\left|A\right|=\left|\begin{array}{ccc}43& 1& 6\\ 35& 7& 4\\ 17& 3& 2\end{array}\right|$
applying $C_1\to C_1-7C_3$
$=\left|\begin{array}{ccc}1& 1& 6\\ 7& 7& 4\\ 3& 3& 2\end{array}\right|=0$
$\therefore$ A is a singular matrix.
$\Rightarrow A^{-1}$ does not exist. ($\because$ The inverse of singular matrix is not possible.)
$\therefore$ Assertion (A) and Reason (R) both are individually true and Reason (R) is correct explanation of Assertion (A).
Hence, option A.