Determinant Calculator calculates the determinant of given matrix. Given are the block  where you can enter the matrix elements you will  get the determinant value instantly.

A determinant is the representation of elements in the square matrix used for solving a system of linear equations or any given matrix. It is represented as

Determinant Formula
Where a11, a12 , a13....... amn are the elements in the given determinant.
Before dealing with the determinant let us understand how to solve the determinant? It has the following steps.
Step-1: Read the given matrix and write it in determinant form.
Step-2: Take the first element from the reference row and column and apply cross multiplication for the  elements excluding that row and column.
Step-3: Then select the second element from the reference row and column and apply cross multiplication for the elements excluding that row and column. 
Step-4: In similar manner do the same process for third element for the reference row and column.
Step-5: Simplify the product and add all of them to get the value of the determinant.

Use the corresponding signs for the determinant based on the position of the elements while carrying out multiplication.

Solved Examples

Question 1: Find the determinant for the given matrix:
$\begin{bmatrix} 2& 4 & 6\\ 1& 2& 3\\ 4& -2& 1 \end{bmatrix}$
Solution:
 
The given Matrix is A = $\begin{bmatrix} 2& 4 & 6\\ 1& 2& 3\\ 4& -2& 1 \end{bmatrix}$
The determinant is given by
|A| = $\begin{vmatrix}
 2& 4 & 6 \\
 1& 2 & 3\\
 4& -2 & 1
\end{vmatrix}$
= 2 $\begin{vmatrix}
 2&3 \\
 2&1
\end{vmatrix}$ - 4 $\begin{vmatrix}
 1&3 \\
 4&1
\end{vmatrix}$ + 6 $\begin{vmatrix}
 1&2 \\
 4&-2
\end{vmatrix}$
= 2(2 - 6) - 4(1 - 12) + 6(-2 - 8).
= 2(-4) - 4 (-11) + 6(-10)
= -8+ 44 - 60
= -24

 

Question 2: Find the determinant of the following matrix: $\begin{vmatrix} 1 & 2\\ 3 & 4 \end{vmatrix}$
Solution:
 
The given matrix is A = $\begin{vmatrix} 1&2 \\ 3&4 \end{vmatrix}$
The determinant of A is given by
|A| = $\begin{vmatrix}
 1&2 \\
 3&4
\end{vmatrix}$
= 1 $\times$ 4 - 3 $\times$ 2
= 4 - 6
= -2.