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Class 12 Maths Chapter 3: Matrices Assertion-reason questions with answers

2 assertion-reason questions on Matrices, 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): For every square matrix A, all the diagonal elements of A − A′ are zero. Reason (R): A − A′ is a skew symmetric matrix, and every diagonal element of a skew symmetric matrix is zero.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

By Theorem 1, (A − A′)′ = A′ − A = −(A − A′), so A − A′ is skew symmetric. In a skew symmetric matrix aii = −aii, so aii = 0. R is true and is exactly why A holds.

Question 2
Assertion (A): For A = [[2, 0], [0, 3]] and B = [[−1, 0], [0, 4]], AB = BA. Reason (R): The product AB of two matrices is defined when the number of columns of A equals the number of rows of B.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

AB = BA = [[−2, 0], [0, 12]]: multiplication of diagonal matrices of the same order is commutative, so A is true. R is the true condition for a product to exist, but it says nothing about AB equalling BA, so it does not explain A.

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