Question

Assertion $\left(A\right)$:
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 $\left(R\right)$:
The inverse of singular matrix is not possible

• A. Both $\left(A\right)$ & $\left(R\right)$ are individually true & $\left(R\right)$ is correct explanation of $\left(A\right)$.
• B. Both $\left(A\right)$ & $\left(R\right)$ are individually true but $\left(R\right)$ is not the correct explanation of $\left(A\right)$.
• C. $\left(A\right)$ is true but $\left(R\right)$ is false.
• D. $\left(A\right)$ is false but $\left(R\right)$ is true

Answer 1

The correct option is A Both $\left(A\right)$ & $\left(R\right)$ are individually true & $\left(R\right)$ is correct explanation of $\left(A\right)$.

$\left|A\right|=\left|\begin{array}{ccc}43& 1& 6\\ 35& 7& 4\\ 17& 3& 2\end{array}\right|$
$\left|A\right|=\left|\begin{array}{ccc}7\times 6+1& 1& 6\\ 7\times 4+7& 7& 4\\ 7\times 2+3& 3& 2\end{array}\right|$
$\left|A\right|=\left|\begin{array}{ccc}7\times 6& 1& 6\\ 7\times 4& 7& 4\\ 7\times 2& 3& 2\end{array}\right|+\left|\begin{array}{ccc}1& 1& 6\\ 7& 7& 4\\ 3& 3& 2\end{array}\right|$
$\left|A\right|=7\left|\begin{array}{ccc}6& 1& 6\\ 4& 7& 4\\ 2& 3& 2\end{array}\right|+\left|\begin{array}{ccc}1& 1& 6\\ 7& 7& 4\\ 3& 3& 2\end{array}\right|=0$
$(\because R_1=R_3,R_1=R_2$ of respective determinants. )
$\therefore$ A is a singular matrix.
$\because$ The inverse of singular matrix is not possible.
$\therefore$ Assertion $\left(A\right)$ and Reason $\left(R\right)$ both are individually true and Reason $\left(R\right)$ is correct explanation of Assertion $\left(A\right)$.