Question

Find the inverse of the matrix $A=\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 1\\ 2& 3& 4\end{array}\right]$

• A. $\left[\begin{array}{ccc}1& 5& 2\\ 3& 1& -2\\ 1& 2& 3\end{array}\right]$
• B. $\left[\begin{array}{ccc}1& 2& 3\\ 1& 5& 9\\ 3& 7& 2\end{array}\right]$
• C. $\left[\begin{array}{ccc}7& 9& 1\\ 3& 5& 7\\ 2& 1& 3\end{array}\right]$
• D. Inverse doesn’t exist

Answer 1

The correct option is D

Inverse doesn’t exist

Give matrix is,

$A=\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 1\\ 2& 3& 4\end{array}\right]$

Lets first find the determinant to use in the equation.

$A^{-1}=\frac{1}{|A|}.Adj\left(A\right).$

If |A| = 0 we can rightway say that the inverse doesn’t exist.

|A|=1(1) - 2 (2) +3(1)

=1 - 4 + 3

= 0

This shows that the given matrix is non-invertible or singular.

Hence the inverse doesn’t exist.