Answer to Question #196879 in Linear Algebra for Mpopo

Question #196879

Give an example of 2 × 2 matrix with non-zero entries that has no inverse.


1
Expert's answer
2021-05-26T14:17:44-0400

If the determinant of a square matrix A is 0, then A has no inverse.

For example


A=(2121)A=\begin{pmatrix} 2 & 1 \\ -2 & -1 \end{pmatrix}

detA=2121=2(1)1(2)=0\text{det}A=\begin{vmatrix} 2 & 1 \\ -2 & -1 \end{vmatrix}=2(-1)-1(-2)=0

The 2x2 matrix A has no inverse.


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