Number associated with a table (or a matrix) of \(n^{2}\) elements used to represent the sum of specific products of the elements in the table.

If there are \(n^{2}\) elements, then there are

*n*rows and*n*columns in the table.Consider the matrix of order 2 : A = \(\begin{pmatrix}a_{1} & b_{1}\\a_{2} & b_{2}\end{pmatrix}\)

The determinant D of this matrix is : D = \(a_{1}b_{2} \space – \space a_{2}b_{1}\)

Cramer’s rule uses the notation of determinant to solve a system of linear equations.

### Example

Consider the matrix of order 2 : B = \(\begin{pmatrix}2 & 3\\-4 & 5\end{pmatrix}\)

The determinant D of this matrix is : D = \(a_{1}b_{2} \space – \space a_{2}b_{1}\) = 10 – (–12) = 10 + 12 = 22