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A square matrix $A$ is said to be invertible if $A$ has an inverse $A^{-1}$ such that $$ AA^{-1} = A^{-1} A = I. $$ For a $2 \times 2$ matrix, $A$ is invertible if and only if $\det A \neq 0$. |
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A square matrix $A$ is said to be invertible if $A$ has an inverse $A^{-1}$ such that $$ AA^{-1} = A^{-1} A = I. $$ For a $2 \times 2$ matrix, $A$ is invertible if and only if $\det A \neq 0$. |