Question

A square matrix A has 9 elements. What is the possible order of A?
A) $1 \times 9$
B) $9 \times 9$
C) $3 \times 3$
D) $2 \times 7$

Answer 1

We know that a square matrix contains the same number of rows as well as same number of columns. So we have to look for the square of a positive integer which gives a result equal to 9. That will be the order of the square matrix.

Complete step-by -step solution:
In this question it is given that a square matrix contains 9 elements.
So to find the possible order of the square matrix first of all we need to find the possible factors of 9.
The factors of 9 are 1,3 and 9.
So, the possible orders of a matrix containing 9 elements are
$1 \times 9$ means 1 row and 9 columns does not form a square matrix
$9 \times 1$ means 9 rows and 1 column does not form a square matrix
$3 \times 3$ means 3 rows and 3 columns forms a square matrix
In a square matrix, the number of rows is equal to the number of columns. So, the required order is 3×3.

Additional information:
Properties of square matrix
A square matrix of order n has n rows and n columns.
A square matrix $\left[ {{a_i}_j} \right]$ is called a symmetric matrix if ${a_{ij}} = {a_{ji}}$, i.e. the elements of the matrix are symmetric with respect to the main diagonal.
A square matrix $\left[ {{a_i}_j} \right]$ is called skew-symmetric if ${a_{ij}} = - {a_{ji}}$
A square matrix is called diagonal if all its elements outside the main diagonal are equal to zero.
A diagonal matrix is called the identity matrix if the elements on its main diagonal are all equal to 1. (All other elements are zero).

Note: A square matrix can only contain the number of elements which has perfect squares. For e.g. 1, 4, 9, 16,25 etc