Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If A is a square matrix such that A^2 = I, then (A - I)^3 + (A + I)^3 - 7A is equal to A. A B. I - A C. I + A D. 3A

If A is a square matrix such that A^2 = I, then (A - I)^3 + (A + I)^3 - 7A is equal to
A. A
B. I - A
C. I + A
D. 3A

Answers (1)

As, (A - I)^3 + (A + I)^3 - 7A

Use a^3 + b^3 = (a + b)(a^2 + ab + b^2)

Also, A^2 = I

(A - I)^3 + (A + I)^3 - 7A

\begin{array}{l} =A^{3}-3 A^{2}+3 A-I^{3}+A^{3}+3 A^{2}+3 A+I^{3}-7 A \\ =2 A^{3}+6 A-7 A \\ =2 A^{2} \cdot A+6 A-7 A \\ =2 I \cdot A+6 A-7 A \\ =2 A+6 A-7 A=8 A-7 A=A \end{array}

∴ then (A - I)^3 + (A + I)^3 - 7A= A

Clearly our answer is similar to option (A)

Hence, we can say that,

∴ option (A) is the correct answer.

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question