KCET 2026 Mathematics Solved Paper

Concept:The determinant has standard multiplicative and scalar properties, but it is not linear under matrix addition.Explanation:For two invertible square matrices $A$ and $B$ of order $n$, the known determinant properties are as follows.$\operatorname{det}(A B)=\operatorname{det}(A) \cdot \operatorname{det}(B)$ is a standard property.So Option A is correct.For a scalar $k$, $\operatorname{det}(k A)=k^{n} \operatorname{det}(A)$, because each of the $n$ rows is multiplied by $k$.So Option B is correct.Since $A A^{-1}=I$, taking determinants gives $\operatorname{det}(A) \operatorname{det}(A^{-1})=\operatorname{det}(I)=1$.Thus $\operatorname{det}(A^{-1})=\frac{1}{\operatorname{det}(A)}$, so Option D is correct.However, $\operatorname{det}(A+B)=\operatorname{det}(A)+\operatorname{det}(B)$ is not a valid general property of determinants.Therefore, the statement that is not correct is Option C.Answer:Option C: $\operatorname{det}(A+B)=\operatorname{det}(A)+\operatorname{det}(B)$ is not correct.