Define Square Matrix with Example

What is Square matrix order?

If a matrix has equal numbers of rows and equal numbers of columns, it is called a square matrix.

Define square matrix with example?

A=\begin{bmatrix}1\end{bmatrix}, B=\begin{bmatrix}1&2\\3&4\end{bmatrix}, C=\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}

If a matrix has the same number of rows and columns then it is called a square matrix. Elements in this matrix is arranged in square shape because of the same number of rows and column that’s why we called this matrix square matrix. Rows are shown by m and columns are shown by n. A Square matrice are matrix can be the order of 1 2 3…n. But it is very difficult to work with the order of 11 and above. Basically, a square matrix is denoted by capital words such as E F G B C Z X

                       Matrix m × n

Here the above matrix shows them rows and n column so. As we know that the order of any matrix is multiply by that matrix rows and column so here the order of this matrix is m×n.

Note: the square shape of the matrix is possible if and only if its number of rows is equal to the number of columns such that m=n

How to Square a Matrix 3×3

A=\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}

In the above matrix, the number of rows is 3

In the above matrix, the number of columns is 3

The number of rows and columns are equal so it is a square matrix.

The order of this Square matrices is 3 -by- 3

Is 2×3 a Square Matrix?

A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}

In the above matrix, the number of rows is 2

In the above matrix, the number of columns is 3

The order of the above matrix is 2 -by 3

In the above matrix, the number of rows and number of columns is not equal so it is not a square matrix.

There are two ways to called a square matrix

  • A square matrix of order m or n
  • mTH or nTH order square matrix

4×4 Square Matrix Example

The order of this matrix is 4 -by- 4. we called this matrix:

A=\begin{bmatrix}1&2&3&4\\5&6&7&8\\9&0&1&2\\3&4&5&6\end{bmatrix}
  1. a Square matrices of order 4
  2. 4 order Square matrices

Square of Matrix 2×2

B=\begin{bmatrix}1&2\\3&4\end{bmatrix}

The order of this matrix is 2 -by 2. We call this matrix as

  1. A Square matrices of order 2
  2. 2 order Square matrices

Can a Square matrix be 1×1?

Order of this matrix is 1-by-1. We call this matrix as:

A=\begin{bmatrix}1\end{bmatrix}
  1. A Square matrices of order 1
  2. 1 order Square matrices

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