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

1 Answer

Toolbox:
  • (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 $|3AB|=3\times 3\times 3\times (15)$
$\qquad\qquad\qquad=27\times 15$
$\qquad\qquad\qquad=405$
Hence True.
answered Mar 27, 2013 by sreemathi.v
 

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