Q. Identify the incorrect statement in respect of two square matrices $A$ and $B$ conformable for sum and product:
A) $t_{r}(A + B) = t_{r}(A) + t_{r}(B)$
B) $t_{r}(\alpha A) = \ \alpha t_{r}(A),\ \alpha \in R$
C) $t_{r}\left( A^{T} \right) = t_{r}(A)$
D) None of these
Explanation
(d)
$A$ is involuntary. Hence,
$A^{2} = I \Rightarrow A = A^{- 1}$
Also,
$(kA)^{- 1} = \frac{1}{k}(A)^{- 1}$
$\Rightarrow \left( \frac{1}{2}A \right)^{- 1} = 2(A)^{- 1} \Rightarrow 2A$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.