For b>0, the martix?

Question

(b 2), is invertible if:
(-b a)

a) a is not equal to 2 b) b is not equal to 2 c) a = 2 d) b=2

Answer 1

A matrix is invertible if it's determinant is non-zero. The determinant of:

b 2
-b a

is b*a - (-b*2) = b*a +2b

This is non-0 when a is not equal to -2. None of the multiple choice answers are correct. Was choice (a) typed correctly ?

Answer 2

A matrix can be inverted if its determinant is non zero. The determinant of the matrix you post is:

ab +2b = b(a+2), the value of this determinant is zero if either b is zero or a=-2, could your choice a) be a is not equal to minus 2?

Answer 3

| b 2|
|-b a| is invertible if ∆ ≠ 0

∆ = ab + 2b = b(a+2) ≠ 0

if b ≠ 0

a +2 ≠ 0 => a ≠ - 2

Answer 4

The matrix A is invertible if det(A) is not 0.
Here det A = ab + 2b = b(a+2).
So all your choices are correct here.