Question
Match List - I with List - II.List - I List - II A. Matrix addition is commutative I. If O is the zero matrix of same order as that of the matrix A, then A + 0 = A = 0 + A B. Matrix addition is associative II. If A, B and C be three matrices of the same order, then (A + B) + C = A + (B + C) C. Existence of additive identity III. If A be any matrix, then A + (-A) = O = (-A) + A D. Existence of additive inverse IV. If A and B be two matrices of the same order then A + B = B + A
Choose the correct answer from the options given below :
This question was previously asked in
CUET PG 2026 Agri-Business Management Question Paper (25-Mar-2026) (Shift 2)
The correct answer is
A-IV, B-II, C-I, D-III
Matching Matrix Addition Properties
This question requires matching the fundamental properties of matrix addition with their respective definitions.
Analyzing Properties of Matrix Addition
- A. Matrix addition is commutative: This property states that the order in which two matrices are added does not change the result. Mathematically, for matrices A and B of the same order, \( A + B = B + A \). This corresponds to definition IV.
- B. Matrix addition is associative: This property states that the grouping of matrices in an addition involving three or more matrices does not affect the sum. For matrices A, B, and C of the same order, \( (A + B) + C = A + (B + C) \). This corresponds to definition II.
- C. Existence of additive identity: This refers to the existence of a unique matrix, the zero matrix (denoted by O), such that adding it to any matrix A results in the matrix A itself. Mathematically, \( A + O = A = O + A \). This corresponds to definition I.
- D. Existence of additive inverse: For every matrix A, there exists a unique matrix, its additive inverse (denoted by -A), such that their sum is the zero matrix O. Mathematically, \( A + (-A) = O = (-A) + A \). This corresponds to definition III.
Final Matching
Based on the analysis, the correct matches are:
- A corresponds to IV
- B corresponds to II
- C corresponds to I
- D corresponds to III
Therefore, the correct option is A-IV, B-II, C-I, D-III.
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