Home
Class 12
MATHS
If A is a square matrix such that A^2=A ...

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

A

A

B

I-A

C

I

D

3A

Text Solution

Verified by Experts

The correct Answer is:
A
`Given A^(2)=A`
`therefore (I+A)^(3)-7A=I^(3)+3I^(3)A +3IA^(2)+A^(3) -7A`
`=I+3A+3A^(2)+A^(3) -7A`
`=I+3A+3A +A.A^(2)-7A`
`=I-A+A.A`
`=I-A+A^(2)`
`=I-A+A=I`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    NAGEEN PRAKASHAN|Exercise Exercise 3.4|18 Videos

  • LINEAR PROGRAMMING

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|9 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If A square matrix such that A^2 = A , then (l+A )^3 -7A is equal to :

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

If A is a square matrix such that A^(2)=A, then (I-A)^(2)+A=

If a square matrix such that A^(2)=A, then (I+A)^(3)-7A is equal to A(b)I-A(c)I (d) 3A

if A is a square matrix such that A^(2)=A, then det (A) is equal to

If A is a square matrix such that A^2 = I, then A^(-1) is equal to (i) I (ii) 0 (iii) A (iv) I+A

If A is a square matrix such that A A^T=I=A^TA , then A is