Question

Let 'A' be a square matrix of order 3 × 3, then |KA| is equal to:

Options

• `k^2 |A|`

• `k^3 |A|`

• `3k |A|`

• `k |A|`

Answer 1

`k^3 |A|`

Explanation:

Since 'A' is a square matrix of order 3 × 3

Let A = `[(a_1, b_1, c_1),(a_2, b_2, c_2),(a_3, b_3, c_3)]`

Then, KA = `[(ka_1, kb_1, kc_1),(ka_2, kb_2, kc_2),(ka_3, kb_3, kc_3)]` ⇒ ∴ |KA|

`[(ka_1, kb_1, kc_1),(ka_2, kb_2, kc_2),(ka_3, kb_3, kc_3)]`

= `k^3 [(a_1, b_1, c_1),(a_2, b_2, c_2),(a_3, b_3, c_3)]`

= `k^3 |A|`

∴ |KA| = `k^3A`