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.

Question

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.

Philoid · Accepted Answer

True

We know that |AB| = |A|. |B| and if A = [a_ij]_3×3, then |k.A| = k³|A|.

∴ |3A| = 27 |AB|

= 27 |A| |B|

= 27 (5) (3)

= 405

Hence proved.

The above statement is true.

State True or False for the statementsIf A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.