We are given that,

is an identity matrix.

We need to find the value of α.

We must understand what an identity matrix is.

An identity matrix is a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeroes.

An identity matrix is denoted by

According to the question,

We know by the property of matrices,

This implies,

a₁₁ = b₁₁, a₁₂ = b₁₂, a₂₁ = b₂₁ and a₂₂ = b₂₂

So, if we have

The corresponding elements of matrices are equal.

That is,

cos α = 1

-sin α = 0

sin α = 0

cos α = 1

Since, the equations are repetitive, take

cos α = 1

⇒ α = cos^-1 1

⇒ α = 0°

Thus, the value of α = 0°.