Question

Assertion :The Inverse of the matrix $A=\left[\begin{array}{ccc}4& 2& 3\\ 8& 5& 2\\ 12& -4& 5\end{array}\right]$ certainly exists. Reason: The matrix A is non singular & every non-singular matrix possesses its inverse.

• 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),

$A=\left[\begin{array}{ccc}4& 2& 3\\ 8& 5& 2\\ 12& -4& 5\end{array}\right]$

$\left|A\right|=4(25+8)-2(40-24)+3(-32-60)=-176\ne 0$

$\Rightarrow$ A is non singular $\Rightarrow A^{-1}$ exist.

$\therefore$ Assertion (A) and Reason.(R) both are individually true and Reason (R) is correct explanation of Assertion(A).