If B is a non-singular matrix and A is a

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

If B is a non-singular matrix and A is a square matrix, then $det (B^{-1}AB)$ is equal to

Options:

$det (A^{-1})$

$det (B^{-1})$

det (A)

det (B)

Correct Answer:

det (A)

Explanation:

We have,

$|B^{-1} AB|=|B^{-1}||A||B|$

$⇒|B^{-1} AB|=\frac{1}{|B|}|A||B|$ $\left[∵|B^{-1}|=\frac{1}{|B|}\right]$

$⇒|B^{-1} AB|=|A|$