AP EAMCET · Maths · Matrices
If \(P\) is a square matrix with \(P^2=P\) and if \(I\) is the unit matrix of the same order as of \(P\) then \((P+I)^4=\)
- A \(I+9 P\)
- B \(I+11 P\)
- C \(I+13 P\)
- D \(I+15 P\)
Answer & Solution
Correct Answer
(D) \(I+15 P\)
Step-by-step Solution
Detailed explanation
\((P+I)^2 = P^2+PI+IP+I^2 = P+P+P+I = 3P+I\) \((P+I)^4 = ((P+I)^2)^2 = (3P+I)^2\) \((3P+I)^2 = (3P)^2+3PI+I(3P)+I^2 = 9P^2+3P+3P+I\) \(= 9P+6P+I = 15P+I\)
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