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Provide Solution For  R. D. Sharma Maths Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions Question 16 Maths Textbook Solution.

Answers (1)

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Answer: The correct option is (C).

Given: A is a Square Matrix and A^{2}=A

Solution:

(I+A)^{3}=I^{3}+A^{3}+3 A^{2} I+3 A I^{2}            \text { (Using the Identity, } \left.(a+b)^{3}=a^{3}+b^{3}+3 a b(a+b)\right)

(I+A)^{3}=I+A^{2}(A)+3 A I+3 A            (‘I’ stands for Identity Matrix)

\begin{aligned} &(I+A)^{3}=I+A+3 A+3 A \\ &(I+A)^{3}=I+7 A \\ &(I+A)^{3}-7 A=I \end{aligned}

So, the correct option is (C).

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