How to determine the order of matrix?

If a matrix has m rows and n columns, its order is said to be m × n (read as ‘m by n’).

**Examples:**

[15 9 -5] is of order 1 × 3;

\(\begin{bmatrix} 7 & -6 \end{bmatrix}\) is of order 2 × 1;

\(\begin{bmatrix} a & b\\ c & d \end{bmatrix}\) is of order 2 × 2;

\(\begin{bmatrix} 8 & a & 5\\ -3 & 15 & b \end{bmatrix}\) is of order 2 × 3.

Clearly, a matrix of the order m × n has mn elements. Hence, if the number of elements in a matrix be prime, it must have one row or one column.

Usually, a matrix is denoted by a capital letter, such as A, B, C, D, M, N, X, Y, Z, etc.

Solved Examples on Order of a Matrix:

**1.** Let M = \(\begin{matrix} 5 & 4 & -3 & \\ 2 & -7 & 8 & \end{matrix}\).

What is the order of the matrix M?

**Solution:**

The order of the matrix A is 2 × 3 because there are 2 rows and 3 columns in the matrix.

**2.** If a matrix has six elements, find the possible orders of the matrix.

**Solution:**

6 = 1 × 6;

6 = 6 × 1;

6 = 2 × 3;

6 = 3 × 2

Therefore, the possible orders of the matrix are 6 = 1 × 6, 6 × 1, 2 × 3 and 3 × 2.

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