Assertion (A) : The inverse of A= ( ll 3 & 4 3 & 5 ) does not exi… - Vidyadip

MCQ

Assertion (A) : The inverse of $A=\left(\begin{array}{ll}3 & 4 \\ 3 & 5\end{array}\right)$ does not exist.
Reason (R) : The matrix $A$ is non-singular.

✓
Both (A) and (R) are true and (R) is the correct explanation of (A).
B
Both (A) and (R) are true but (R) is not the correct explanation of (A).
C
(A) is true but (R) is false.
D
(A) is false but (R) is true.

✓

Answer

Correct option: A.

Both (A) and (R) are true and (R) is the correct explanation of (A).

(a) : $\because|A|=\left|\begin{array}{ll}3 & 4 \\ 3 & 5\end{array}\right|=15-12=3 \neq 0$
$\therefore \quad A$ is non-singular.
$\therefore \quad A^{-1}$ exists.

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