Question

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 + 1)^4 =
1) I +9P
2) I + IIP
3) 1 + 13P
4) 1 + 15P​

Answer 1

Answer:

answer is option 2 this is answer of question

Answer 2

Answer:

(4)The value of the given expression is $(P+I)^{4}=I+15P$

Step-by-step explanation:

Given that,

P is a square matrix with an relation provided as $P^{2}=P$ And I is a unit matrix of same order as that of P.We are required to find the value of $(P+I)^{4}$

The above expression can be written in the way as shown below

$(P+I)^{4}=[(P+I)^{2}]^{2}$

By squaring the expression we obtain terms as shown below

$(P^{2}+I^{2}+2PI)^{2}$

From the given question,we know that $P^{2}=P\\I^{2}=I$By substituting these values in above mentioned expression,the expression becomes -

$(P+I+2P)^{2}=(3P+I)^{2}\\=9P^{2}+I^{2}+6PI=9P+I+6P\\=15P+I$

Therefore,the value of the given expression is $(P+I)^{4}=I+15P$

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