MyQuestionIcon

1

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

Inverse of a Matrix

If A and B ar...

Question

If A and B are square matrices of the same order such that AB = BA, then show that (A + B)² = A² + 2AB + B².

Open in App

Solution

(A + B)² = (A + B)(A + B)
= A² + AB + BA + B²
= A² + 2AB + B² (∵ AB = BA)

Hence, (A + B)² = A² + 2AB + B².

Suggest Corrections

thumbs-up

7

Similar questions

Show that if A and B are square matrices such that AB = BA, then $(A + B)^{2} = A^{2} + 2 A B + B^{2}$ .

A

B

are square matrices of the same order such that

A^{2} = A, B^{2} = B, A B = B A = 0

Q. If A and B are square matrices of the same order, explain, why in general
(i) (A + B)² ≠ A² + 2AB + B²
(ii) (A − B)² ≠ A² − 2AB + B²
(iii) (A + B) (A − B) ≠ A² − B².

Q. If A and B are square matrices of the same order, then (A + B)(A − B) is equal to

(a) A² − B²
(b) A² − BA − AB − B²
(c) A² − B² + BA − AB
(d) A² − BA + B²+ AB

Q. If A, B are two square matrices such that

A B = A

B A = B

, then prove that

B^{2} = B

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

Inverse of a Matrix

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon