If A and B are two $$non-singular$$ matrices of order $$3$$ such that $$AAT=2I$$ and A−$$1=AT$$−A . adj $$2B$$−$$1$$ , then det⁡ (B) equals

Question

If A and B are two $$non-singular$$ matrices of order $$3$$ such that $$AAT=2I$$ and A−$$1=AT$$−A . adj $$2B$$−$$1$$ , then det⁡ (B) equals

Infinity Learn · Accepted Answer

Given that $$AAT=2I$$⇒|A|$$2=8$$ And A−$$1=AT$$−A adj⁡$$2B$$−$$1$$⇒$$I=AAT$$−$$A2adj$$⁡$$2B$$−$$1$$⇒$$I=2I$$−$$A2adj$$⁡$$2B$$−$$1$$⇒$$A2$$ adj $$2B$$−$$1=I$$⇒$$A2$$∥adj⁡$$2B$$−$$1=1$$⇒$$82B$$−$$12=1$$        ∵ adj $$A=An-1$$⇒$$8$$×$$64$$|B|$$2=1$$         ∵ $$B-1=1Band$$ $$kA=k3A=23B-12$$⇒|B|$$2=64$$×$$8$$∴|B|$$=$$±$$162$$

$If A and B are two non-singular matrices of order 3 such that {AA}^{T} = 2 I and$ $A^{- 1} = A^{T} - A . adj (2 B^{- 1}), then \det (B) equals$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If A and B are two non-singular matrices of order 3 such that AAT=2I and A−1=AT−A . adj 2B−1 , then det⁡ (B) equals

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$If A and B are two non-singular matrices of order 3 such that {AA}^{T} = 2 I and$ $A^{- 1} = A^{T} - A . adj (2 B^{- 1}), then \det (B) equals$