Question

If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.

Options

• 1 + a² + bc = 0 

• 1+ a² - bc = 0 

• a² + bc = 1 

• 1 - a² + bc = 0 

Answer 1

If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation a² + bc = 1.

Explanation:

`[("a","b"),("c", "-a")] [("a","b"),("c", "-a")] = [(1,0),(0,1)]`

`=> "a"^2 + "bc" = 1`