CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Adjoint of a Matrix

If A is a squ...

Question

If A is a square matrix $A^{2} = A$ show that $(I + A)^{3} = 7 A + I$

Open in App

Solution

$(I + A)^{3} - 7 A = I^{3} + A^{3} + 3 I^{2} A + 3 A^{2} I - 7 A$
$= I + A^{3} + 3 A + 3 A^{2} - 7 A$
$= I + A^{2} . A + 3 A + 3 A - 7 A$ [ $A^{2} = A$ ]
$= I + A . A - A$
$= I + A - A$
$= I$
$∴ (I + A)^{3} - 7 A = I$

Suggest Corrections

thumbs-up

1

Similar questions

A

is a square matrix such that

A^{2} = A

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

A

is square matrix such that

A^{2} = A

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

Q. If A is a square matrix such that A² = A, then (I + A)³ − 7A is equal to
(a) A
(b) I − A
(c) I
(d) 3A

Q. If A is a square matrix such that A² = A, then write the value of 7A − (I + A)³, where I is the identity matrix.

A

is a square matrix,such that

A^{2} = A

, then write the value of

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

I

is an identity matrix.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Adjoint and Inverse of a Matrix

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Adjoint of a Matrix

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon