Question

If $A$ is a scalar matrix $kI$ with scalar $k\ne 0$ of order $3$, the $A^{-1}$ is:

• A. $\frac{1}{k^2}I$
• B. $\frac{1}{k^3}I$
• C. $\frac{1}{k^{}}I$
• D. $kI$

Answer 1

The correct option is C $\frac{1}{k^{}}I$

If $A$ is a scalar matrix with scalar $k$, then $A=kI$

Thus $A^{-1}=(kI{)}^{-1}=\frac{1}{k}I$

Note: Inverse of identity matrix is Identity matrix itself

And $(kA{)}^{-1}=\frac{1}{k}{I}^{-1}=\frac{1}{k}I$