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Class 12 Maths Chapter 4: Determinants Assertion-reason questions with answers

2 assertion-reason questions on Determinants, each with its answer and the reason, written from the NCERT chapter. For the CBSE board and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): The matrix [[2, 4], [1, 2]] has no inverse. Reason (R): A square matrix is invertible if and only if it is nonsingular.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

|[[2, 4], [1, 2]]| = 4 − 4 = 0, so the matrix is singular; by the theorem in R it is not invertible. Both are true and R explains A.

Question 2
Assertion (A): For every square matrix A of order 3, |3A| = 27|A|. Reason (R): A determinant is most easily evaluated by expanding along the row or column with the most zeros.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

A is true, since |kA| = kⁿ|A| with n = 3 and k = 3. R is a true remark on calculation, but it says nothing about why the factor is 33.

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