A matrix that consists of the entries (or elements) in three rows and three columns is called a $3 \times 3$ matrix.

A $3 \times 3$ matrix is a special matrix. It is very useful in mathematics. So, it is very important to study what a $3 \times 3$ matrix is. So, let’s learn the $3 \times 3$ matrix in detail.

The following matrix $M$ represents a $3 \times 3$ matrix.

$M$ $\,=\,$ ${\begin{bmatrix} e_{11} & e_{12} & e_{13} \\ e_{21} & e_{22} & e_{23} \\ e_{31} & e_{32} & e_{33} \\ \end{bmatrix}}$

In a matrix of the order $3$, it has total nine elements and they are arranged in three rows and three columns. The arrangement of the nine entries forms a square shape inside the matrix. Hence, it is also called a square matrix of the order $3$.

The following three matrices are some examples for a $3 \times 3$ square matrix.

$(1).\,\,\,$ ${\begin{bmatrix} 4 & 7 & 2 \\ 5 & 3 & 8 \\ 1 & 4 & 6 \\ \end{bmatrix}}$

$(2).\,\,\,$ ${\begin{bmatrix} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \\ \end{bmatrix}}$

$(3).\,\,\,$ ${\begin{bmatrix} 3 & 0 & 0 \\ 7 & 2 & 0 \\ 1 & 6 & 4 \\ \end{bmatrix}}$

The determinant of a third order matrix is simply written as $\operatorname{det}(M)$ or $|M|$, and it is expressed in matrix form as follows.

$|M|$ $\,=\,$ ${\begin{vmatrix} e_{11} & e_{12} & e_{13} \\ e_{21} & e_{22} & e_{23} \\ e_{31} & e_{32} & e_{33} \\ \end{vmatrix}}$

There is a special procedure for determining the determinant of a square matrix of the order $3$. So, let’s learn how to find the determinant of any $3 \times 3$ matrix in mathematics.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.