If A and B are square matrices of order 3 such that |A| = -1, |B| = 3,

1.	If A and B are square matrices of order 3 such that \|A\| = -1, \|B\| = 3, then find the value of \|3AB\|.
Answer» We are given that, A and B are square matrices of order 3. \|A\| = -1, \|B\| = 3 We need to find the value of \|3AB\|. By property of determinant, \|KA\| = Kⁿ\|A\| If A is of n^th order. If order of A = 3 × 3 And order of B = 3 × 3 ⇒ Order of AB = 3 × 3 [∵, Number of columns in A = Number of rows in B] We can write, \|3AB\| = 3³\|AB\| [∵, Order of AB = 3 × 3] Now, \|AB\| = \|A\|\|B\|. ⇒ \|3AB\| = 27\|A\|\|B\| Putting \|A\| = -1 and \|B\| = 3, we get ⇒ \|3AB\| = 27 × -1 × 3 ⇒ \|3AB\| = -81 Thus, the value of \|3AB\| = -81.

If A and B are square matrices of order 3 such that |A| = -1, |B| = 3, then find the value of |3AB|.

Answer»

We are given that,

A and B are square matrices of order 3.

|A| = -1, |B| = 3

We need to find the value of |3AB|.

By property of determinant,

|KA| = Kⁿ|A|

If A is of n^th order.

If order of A = 3 × 3

And order of B = 3 × 3

⇒ Order of AB = 3 × 3

[∵, Number of columns in A = Number of rows in B]

We can write,

|3AB| = 3³|AB| [∵, Order of AB = 3 × 3]

Now, |AB| = |A||B|.

⇒ |3AB| = 27|A||B|

Putting |A| = -1 and |B| = 3, we get

⇒ |3AB| = 27 × -1 × 3

⇒ |3AB| = -81

Thus, the value of |3AB| = -81.