Question

Consider the following in respect of two non-singular matrices $A$ and $B$ of same order:
$1.det(A+B)=detA+detB$
$2.(A+B{)}^{-1}=A^{-1}+B^{-1}$
Which of the above is/are correct?

• A. $1$ only
• B. $2$ only
• C. Both $1$ and $2$
• D. Neither $1$ nor $2$

Answer 1

The correct option is D Neither $1$ nor $2$

$f(A+B)=f\left(A\right)+f\left(B\right)$ only if the function is a linear function.

But here determinant and inverse functions are non-linear functions

$\therefore$ both are incorrect (Neither 1 nor 2)