AP EAMCET · Maths · Matrices
In \(P\) and \(Q\) are square matrices such that \(P^{2006}=0\) and \(P Q=P+Q\), then \(\operatorname{det}(Q)\) will be
- A 0
- B 1 only
- C -1 only
- D \pm 1
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
\begin{array}{llll} & P^{2006} =O \text { and } P Q=P+Q \\ \Rightarrow & P^{2006} Q =P^{2006}+Q \cdot P^{2005} \\ \Rightarrow & O =O+Q \cdot P^{2005} \\ \Rightarrow & P^{2005} \cdot Q =O \\ \Rightarrow & \operatorname{det} \cdot\left(P^{2005} \cdot Q\right) =O \\ \Rightarrow &…
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