Q51 of 58 Page 77

State True or False for the statements

If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.

True

We know that |AB| = |A|. |B| and if A = [aij]3×3, then |k.A| = k3|A|.


∴ |3A| = 27 |AB|


= 27 |A| |B|


= 27 (5) (3)


= 405


Hence proved.


The above statement is true.


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