CUET · MATHS · PYQ PAPER 2023

The number of square matrices of order 2 using numbers 1 and -1 exactly once and the number 0 twice is :

A 24
B 9
C 12
D 6

Verified Solution

Answer & Solution

Correct Answer

(C) 12

Step-by-step Solution

Detailed explanation

Number of ways to choose positions for 1 and -1, then arrange them: \( P(4,2) \). Remaining positions filled by 0s: \( 1 \). Total number of matrices = \( P(4,2) = \frac{4!}{(4-2)!} = \frac{4 \times 3 \times 2 \times 1}{2 \times 1} = 12 \).

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.

Same subject

Match List-l with List-ll
Let \(A\) be any invertible square matrix. Then

List-l	List-ll
(A) \(A-A^T\)	(I) \(\|A\| A^{-1}\)
(B) \(A A^T\)	(II) Skew-symmetric
(C) \(\operatorname{det}\left(A^{-1}\right)\)	(III) Symmetric
(D) \(\operatorname{adj} A\)	(IV) \([\operatorname{det}(A)]^{-1}\)

Choose the correct answer from the options given below :

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List - I	List - II
(A) \(M_{23}\)	(I) -17
(B) \(A_{32}+a_{13}\)	(II) -1
(C) \(A\) (Determinant value)	(III) 0
(D) \(a_{13} A_{12}+a_{23} A_{22}+a_{33} A_{32}\)	(IV) 12