Question

Let $AX=B$ be a system of n-linear equations in n unknowns then

• A. System is consistent and infinitely many solution if $|A|=0.$
• B. System is inconsistent and finitely many solution if $|A|=0$.
• C. System is consistent and unique solution if $|A|\ne0.$
• D. System is consistent if $|A|=0$ and (adj A) $B\ne0$.

Hint:

Cramer's Rule and Matrix Inverse method only work when $|A| \neq 0$. If you see $|A| \neq 0$ in a question about consistency, "unique solution" is almost always the intended answer.

Answer 1

The Correct Option is C