Question

if A is an identity matrix of order 3 , then it's inverse is ​

Answer 1

Answer:

$A^{-1}=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

Step-by-step explanation:

Formula used:

The inverse of a square A is

$\frac{1}{|A|}(adjA)$

Given:

$A=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

$|A|=1(1-0)-0(0-0)+0(0-0)$

$|A|=1\neq0$

Therefore,

$A^{-1}$ exists

Cofactor matrix of A

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

adjoint of A = Transpose of cofactor matrix of A

$adjA=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

Now,

$A^{-1}=\frac{1}{|A|}(adjA)$

$A^{-1}=\frac{1}{1}\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

$A^{-1}=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$