Question

How do you find the Determinant of a Square Matrix?

Answer 1

Finding the determinant of a square matrix:

There is a 2-step procedure to determine the determinant of a square matrix:

Pick any row or a column in the matrix. This is because the answer will remain the same for any row or column.

Every element in the selected row or column should be multiplied by its cofactor and then added.

The result so obtained is the determinant.

Determinant is a scalar value that can be calculated from the elements of a square matrix.

It is an arrangement of numbers in the form

$\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$

Determinant for a $3\times 3$ matrix is determined by

$\begin{array}{c}\begin{array}{c}\begin{array}{c}\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|\begin{array}{}\\ \\ \end{array}\end{array}\end{array}\end{array}$

$=a_1(b_2{c}_3-b_3{c}_2)-b_1(a_2{c}_3-a_3{c}_2)+c_1(a_2{b}_3-a_3{b}_2).$

Hence, in this way we can find the determinant of a square matrix.