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.