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`

A

A

B

I-A

C

I

D

3A

Text Solution

Verified by Experts

`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

Similar Questions

Explore conceptually related problems

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

If A is a square matrix such that A^2=A ,t h e n(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=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

If A is a square matrix such that A^2=A , show that (I+A)^3=7A+I .

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 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=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

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