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 two square matrices such that $B = - A^{- 1} B A,$ then $(A + B)^{2}$ is equal to

A^{2} + B^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

A^{2} - B^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A^{2} + 2 A B + B^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A + B

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $A^{2} + B^{2}$
As $B = - A^{- 1} B A,$
$\Rightarrow A B = - B A \Rightarrow A B + B A = O$

Now,
$(A + B)^{2} = (A + B) (A + B)$
$= A^{2} + A B + B A + B^{2}$
$= A^{2} + O + B^{2} = A^{2} + B^{2}$

Suggest Corrections

Similar questions

B = - A^{- 1} B A,

(A + B)^{2}

A

B

B = - A^{- 1} B A,

(A + B)^{2}

B = - A^{- 1} B A

(A + B)^{2} = A^{2} + B^{2}

A

B

B = - A^{- 1} B A

(A + B)^{2} =

Join BYJU'S Learning Program