You visited us 14 times! Enjoying our articles? Unlock Full Access!

Multiplication of Matrices

If B = ABA-...

Question

If $B = A B A^{- 1}$ then $A B A^{- 1}$ equals

A^{- 1} B A

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

A^{- 1} B^{- 1} A

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

A B A

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

B^{- 1} A^{- 1}

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

Open in App

Solution

The correct option is D $A^{- 1} B A$
Given, $B = A B A^{- 1}$
$A^{- 1} B = (A^{- 1} A) B A^{- 1}$
$\Rightarrow A^{- 1} B = B A^{- 1}$
$∴ A^{- 1} B A = B A^{- 1} A$
Hence, $A^{- 1} B A = B = A B A^{- 1}$

Suggest Corrections

Similar questions

A

n \times n

3 A B A^{- 1} + A = 2 A^{- 1} B A,

\frac{a + b + c}{a^{- 1} b^{- 1} + b^{- 1} c^{- 1} + c^{- 1} a^{- 1}} = a b c

{(a^{- 1} + b^{- 1})}^{- 1} = \frac{a b}{a + b}

A = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦

B = [\begin{matrix} - 2 & - 1 & - 4 \end{matrix}],

(A B) A

Solve for x:

\frac{x}{a} + \frac{x}{b} = 1

{log}_{245} 175 = a

{log}_{1715} 875 = b

\frac{1 - a b}{a - b}

Join BYJU'S Learning Program