Question

Which among the following are singular matrix /matrices?

• A. $\left[\begin{array}{cc}1& 0\\ 1& 0\end{array}\right]$
• B. $\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$
• C. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
• D. $\left[\begin{array}{cc}1& 1\\ 0& 0\end{array}\right]$

Answer 1

Answer: (A), (B), (D)

$\left[\begin{array}{cc}1& 1\\ 0& 0\end{array}\right]$

For checking if a matrix is singular or not we just need to check if the determinant is zero or not. If determinant is zero then the matrix is singular or an inverse doesn’t exist for that matrix. If determinant is not zero then it’s a non-singular matrix.

Also remember, for a 2 $\times$ 2 matrix determinant is taken by the following formula

determinant of matrix $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ = ad - bc.

If you calculate the determinants for options a), b) and d) you will get determinant as 0. So these matrices are singular or non invertible. Only for option c) which is an identity matrix you will get determinant as a non zero number .Hence its non singular. Correct options are hence a,b and d.