Question

For a square matrix A and a non-singular matrix B of the
same order, the value of det(
B inverse AB) is:
options a. |A| b. |A inverse| c. |B| d. |B inverse| ​

Answer 1

Answer:

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

$\sf{The \: value \: of \: \: det( {B}^{ - 1} AB)}$

for a square matrix A and a non-singular matrix B of the same order

PROPERTIES ON DETERMINANT

1. For two square matrices A and B

$\sf{det(A B) = det \:( A )\times det \: ( B )\: }$

2. If A is a non-singular square matrix then

$\displaystyle \sf{det({A}^{ - 1}) = \frac{1}{det \: (A)} \: }$

CALCULATION

$\sf{det( {B}^{ - 1} AB)}$

$= \sf{det( {B}^{ - 1}) \times det( A) \times det(B)} \: \: ( \: by \: property \: 1)$

$= \displaystyle \sf{ \frac{1}{det \: (B)} \times det(A) \times det(B) \: } \: \: \: (\: by \: property \: 2 \: )$

$= \displaystyle \sf{ det(A) \: }$

RESULT

$\boxed{ \: \sf{det( {B}^{ - 1} AB) \: \: = det( A) } \: \: \: }$

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LEARN MORE FROM BRAINLY

Represent all possible one-one functions from the set A = {1, 2} to the set B = {3,4,5) using arrow diagram.

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