I have a question about this matrix: $\begin{bmatrix}a & b\\c & d\end{bmatrix}$

Show that if $D = ad − cb$ does not equal $0$, then $A^{-1}$ = $D^{-1}*\begin{bmatrix}d & -b\\-c & a\end{bmatrix}$

How do I show this? Can someone help?

  • 4
    $\begingroup$ Hint: multiply the first matrix by the second. $\endgroup$ – Gribouillis Dec 14 '17 at 13:40

By definition, the inverse matrix $A^{-1}$ satisfies $$ A A^{-1} = A^{-1} A = I $$ where $I$ is the (in this case, $2\times 2$) identity matrix. To show the matrix $B = \frac{1}{D}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$ is equal to $A^{-1}$, it suffices to show $AB = I$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.