Question

If Ais any symmetric matrix, then detA = 1 or det A = -1.

Short answer

Therefore, det A = 0 the given statement is not satisfied.

Step-by-step solution

Matrix Definition

Matrix is a set of numbers arranged in rowsand columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “$m\times n$.”

To check whether the given condition is true or false

For example,

$A=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$

$detA=1-1$.

is a symmetric matrix, yet $detA=0$.

Therefore, the given statement is false.