determinant det(2AB) : Let A and B be (3 xx 3) matrices with det A = 4 and det B = 3. What is det (2AB) equal to ?

 determinant det(2AB) :  Let A and B be (3 xx 3) matrices with det A = 4 and det B = 3. <br> What is det (2AB) equal to ?

Let A and B be (3 xx 3) matrices with det A = 4 and det B = 3. <br> What is det (2AB) equal to ?

https://www.doubtnut.com/question-answer/let-a-and-b-be-3-xx-3-matrices-with-det-a-4-and-det-b-3-what-is-det-2ab-equal-to--59995474

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Updated On: 3-12-2020

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Text Solution

A

96

B

72

C

48

D

36

Answer

A

Solution

A and B are (3×3)${\displaystyle (3\times 3)}$ matrices
det A = 4
det B = 3
∴det(2AB)=(2)3|A||B|${\displaystyle \therefore \det \left(2AB\right)={\left(2\right)}^3\left|A\right|\left|B\right|}$
=23(4)(3)=8(4)(3)=96