If A, B and C are 3 invertible matrices and BAC = I, what is the value of A.

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

C^{- 1} B^{- 1}

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

B^{- 1} C^{- 1}

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

A^{- 1}

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

Open in App

Solution

The correct option is C $B^{- 1} C^{- 1}$
Given that,
BAC = I
Premultiplying equation with $B^{- 1}$
$B^{- 1} B A C = B^{- 1}$
$i . e ., A C = B^{- 1}$
Post multiplying equation by $C^{- 1}$
$A C C^{- 1} = B^{- 1} C^{- 1}$
$A = B^{- 1} C^{- 1}$

Suggest Corrections

Similar questions

adj A = |A| A^{- 1}

\det (A^{- 1}) = {(\det A)}^{- 1}

{(A + B)}^{- 1} = A^{- 1} + B^{- 1}

{(A B)}^{- 1} = B^{- 1} A^{- 1}

|A|

A, B

C

B A C = I,

A

Join BYJU'S Learning Program