CUET · MATHS · PYQ PAPER 2025

For the system of equations \(A X=B\), which of the following is correct?

A If \(A\) is a singular matrix, then \(A X=B\) has a unique solution.
B If \(A\) is a non-singular matrix, then \(A X=B\) has infinitely many solutions.
C If \(A\) is a non-singular matrix, then \(A X=B\) has a unique solution.
D If \(A\) is a singular matrix, then \(A X=B\) is always consistent.

Verified Solution

Answer & Solution

Correct Answer

(C) If \(A\) is a non-singular matrix, then \(A X=B\) has a unique solution.

Step-by-step Solution

Detailed explanation

If \(A\) is a non-singular matrix, then \(A^{-1}\) exists. \(AX=B \implies X = A^{-1}B\). Thus, \(A X=B\) has a unique solution.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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