Question 21 markMCQSection A

Which of the following cannot be the order of a row-matrix?

Matrices
Order of a Row Matrix

Options

(A)2×12 \times 1
(B)1×21 \times 2
(C)1×11 \times 1
(D)1×n1 \times n

Official answer

Correct option: (A) 2×12 \times 1


A row matrix has exactly 1 row, so its order must always be of the form 1×n1 \times n. An order of 2×12 \times 1 describes a matrix with 2 rows and 1 column, which is a column matrix, not a row matrix.

Answer keywords:row matrixcolumn matrixorder of matrix1 x nmatrix definitionsrows and columns

Marking scheme

  1. 1.1 mark: correct option (A) selected.

Hint

A row matrix must have exactly one row — its order is always written as 1×n1 \times n, never m×1m \times 1.

Quick oral answer

A row matrix always has exactly one row, so its order is 1×n1 \times n; 2×12 \times 1 has two rows, making it a column matrix instead, so the answer is (A).

Common mistakes

  1. 1.Confusing row matrix (1×n1 \times n) with column matrix (m×1m \times 1) and picking (D) by mistake.
  2. 2.Assuming a 1×11\times1 matrix cannot be a row matrix, when in fact it satisfies both row and column matrix definitions simultaneously.

Analysis and explanation

This checks the basic definition of a row matrix versus a column matrix.


Concept

  • A row matrix is defined as a matrix having exactly one row, so its order is always 1×n1 \times n for some positive integer n.
  • A column matrix has exactly one column, with order m×1m \times 1.

Why (A) is correct

  • 2×12 \times 1 means 2 rows and 1 column — this describes a column matrix, so it can never be the order of a row matrix.

Why the other options are wrong

  • (B) 1×21 \times 2 has 1 row and 2 columns — a valid row matrix.
  • (C) 1×11 \times 1 has 1 row and 1 column — technically satisfies the 1×n1 \times n form with n = 1, so it is a valid (trivial) row matrix.
  • (D) 1×n1 \times n is exactly the general form of a row matrix's order, so it is always valid.

Interesting facts

A 1×11\times1 matrix is the only type of matrix that is simultaneously a row matrix, a column matrix, a square matrix, a diagonal matrix, and a scalar matrix.

Row and column matrices are the building blocks of vectors in linear algebra — a row matrix represents a row vector, commonly used in coordinate geometry and computer graphics transformations.

Question details

Q2 of 44 questions

Board
CBSE
Class
Class 12
Subject
Mathematics
Year
2026
Section
Section A
Marks
1
Type
MCQ
Chapter
Matrices
Topic
Order of a Row Matrix
Bloom's level
remember
Syllabus topic
Unit II: Algebra — Matrices: Order of a Matrix
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

What is the difference between a row matrix and a column matrix?

A row matrix has exactly one row and order 1×n1 \times n, while a column matrix has exactly one column and order m×1m \times 1. They represent different arrangements of the same number of elements.

Can a matrix be both a row matrix and a column matrix?

Yes, only a 1×11\times1 matrix satisfies both definitions simultaneously, since it has exactly one row and exactly one column.