Question

Let A be a square matrix of order 2 x 2, then `abs("KA")` is equal to ____________.

Options

• `"K" abs "A"`

• `"K"^2 abs "A"`

• `"K"^3 abs "A"`

• `2"K" abs "A"`

Answer 1

Let A be a square matrix of order 2 x 2, then `abs("KA")` is equal to `underline("K"^2 abs "A")`.

Explanation:

as if A `= [("a","b"),("c","d")]` then `abs "A" = abs(("a","b"),("c","d"))`

KA `= [("Ka","Kb"),("Kc","Kd")]  "and"  abs"KA" = abs (("Ka","Kb"),("Kc","Kd"))`

`= "K"^2 abs (("a","b"),("c","d")) = "K"^2 abs "A".`