Answer :

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°.


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