Given A is a 2×2 matrix,

So let

Here I₂ is an identity matrix of size 2,

So the given equation becomes,

To satisfy the above equality condition, corresponding entries of the matrices should be equal, i.e.,

a + b = 6…….(i)

– 2a + 4b = 0 ⇒ 2a = 4b ⇒ a = 2b……..(ii)

c + d = 0 ⇒ c = – d……(iii)

– 2c + 4d = 6 ……(iv)

Substitute the values of eqn(ii) in eqn (i), we get

a + b = 6 ⇒ 2b + b = 6 ⇒ b = 2

So eqn(ii) becomes, a = 2b = 2(2) = 4⇒ a = 4

Substitute the values of eqn(iii) in eqn (iv), we get

– 2c + 4d = 6 ⇒ – 2( – d) + 4d = 6 ⇒ 2d + 4d = 6 ⇒ 6d = 6 ⇒ d = 1

So eqn(iii) becomes, c = – d⇒ c = – 1

Now substituting these values in matrix A, we get

is the matrix A.