If A and B are square matrices of the same order such that A = - B - 1 A B , then A + 3 B 2 is equal to

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Question: Answered & Verified by Expert

If

A

and

B

are square matrices of the same order such that

A = - B^{- 1} A B

, then

{(A + 3 B)}^{2}

is equal to

MathematicsMatricesJEE Main

Options:

A $A + 3 B$
B $A^{2} + 9 B^{2}$
C $A^{2} + 6 A B + A B^{2}$
D $O$

Solution:

1941 Upvotes Verified Answer

The correct answer is:

A^{2} + 9 B^{2}

A = - B^{- 1} A B \Rightarrow B A = - A B \Rightarrow B A + A B = 0

{(A + 3 B)}^{2} = A^{2} + 9 B^{2} + 3 A B + 3 B A = A^{2} + 9 B^{2}

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