# If A is invertible matrix of order $3\times 3$,then $| A^{-1} |$___________.

## 1 Answer

Toolbox:
• A square matrix is invertible if it is non-singular.
If A is invertible matrix of order $3\times 3$,then |A|$\neq 0$
The determinant of a matrix should not be equal to zero,it has an inverse.
$A.A^{-1}=I$
$\Rightarrow A^{-1}=\frac{1}{A}.I$
Take determinant on both sides,
$|A^{-1}|=\frac{1}{|A|}|I|$
But |I|=1.
Therefore $|A^{-1}|=\frac{1}{|A|}$
answered Mar 26, 2013

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