Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Determinants
0 votes

True or False: If A and B are matrices of order 3 and $\mid A\mid=5,\mid B \mid=3,then\mid 3AB\mid=27\times 5\times 3=405$

Can you answer this question?

1 Answer

0 votes
  • (i) The determinant of the product of matrices is equal to product of the respective determinant ,that |AB|=|A||B|,where A and B are the square matrices of the same order.
  • (ii) $|kA|=k^3|A|$
Given: |A|=5,|B|=3
Therefore |AB|=|A||B|
$\qquad\qquad\quad=5\times 3=15.$
$|3AB|=3^3|AB|$ $\qquad(|kA|=k^3|A|)$
Therefore $|3AB|=3\times 3\times 3\times (15)$
$\qquad\qquad\qquad=27\times 15$
Hence True.
answered Mar 27, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App