Question

Match List - I with List - II:

• A. A-I, B-II, C-III, D-IV
• B. A-II, B-IV, C-III, D-I
• C. A-IV, B-III, C-II, D-I
• D. A-IV, B-II, C-I, D-III

Hint:

Logic Tip: Identity gives A + O = A (statement I) and inverse gives A + (-A) = O (statement III).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:

• We must match each property of matrix addition in List - I with its statement in List - II.

Step 2: Detailed Explanation:

• A. Matrix addition is commutative: A + B = B + A, which is statement IV.
• B. Matrix addition is associative: (A + B) + C = A + (B + C), which is statement II.
• C. Existence of additive identity: A + O = A = O + A for the zero matrix O, which is statement I.
• D. Existence of additive inverse: A + (-A) = O = (-A) + A, which is statement III.
• So the matching is A-IV, B-II, C-I, D-III.

Step 3: Final Answer:
The correct option is (D) A-IV, B-II, C-I, D-III.