Question

The value of an even order skew symmetric determinant is

Answer 1

Hint: The determinant can be defined as the scalar value which can be calculated from the elements of a square matrix and converts certain properties of the linear transformation. The determinant is denoted by det(A), det A, or |A|.

Complete step-by-step answer:
In linear and the multilinear algebra, the determinant is connected with the element of a square matrix with “n” number of rows and the “n” number of columns.
The order of the matrix is symbolized by $ 2 \times 2 $ with two rows and two columns and likewise it is denoted by $ 3 \times 3 $ for three rows and three columns.
Skew Symmetric determinant – Skew symmetric determinant is defined as the elements in each column of the matrix that are equal to the matrix are equal to the elements corresponding to the row of the matrix with the changed signs.
For Example –
Let matrix $ A = \left| {\begin{array}{*{20}{c}}
  0&a \\
  { - a}&0
\end{array}} \right| $ the even order skew symmetric matrix
Now, expanding the above determinant –
 $ \left| A \right| = 0 - (a)( - a) $
Simplifying the above expression, the product of two negative terms is always positive.
 $ \left| A \right| = {a^2} $
Hence, the determinant of the even order skew symmetric determinant is the whole square.

Note: Do not get confused between the determinants and the matrices. Determinant is defined as the square matrix with the same number of rows and columns whereas, the matrices can be defined as the rectangular grid of numbers and number of rows and the columns may not be the same.