Question

For any matrix A and B other than identity matrix if AB=B and BA=A and (A+B)^3 = K (A+B), Find K ?​

Answer 1

Step-by-step explanation:

given :

For any matrix A and B other than identity matrix if AB=B and BA=A and (A+B)^3 = K (A+B), Find K ?

to find :

if AB=B and BA=A and (A+B)^3 = K (A+B), Find K ?

solution :

• A²+ B² = AA + BB

• = A(BA) + B(AB) (Given AB =

• B and BA = A)

• (AB)A + (BA)B

• = BA + AB

• = A + B

• the answer is A+ B

Answer 2

Given:

Matrix A and B.

AB=B and BA=A,

(A+B)³ = K (A+B).

To Find:

Find the value of K.

Solution:

By the identity,

A²+ B² = AA + BB.

We know that,

AB = B and BA = A.

A² + B² = A(BA) + B(AB).

A² + B² = (AB)A + (BA)B.

A² + B² = BA + AB

A² + B² = A + B

Hence, the value of K is (A + B).