If and A^–1 = A’, find value of α.

Given, A =

We know that transpose of a matrix is obtained by interchanging rows with respective columns.

∴ A’ =

Inverse of a matrix A = A^-1 =

Clearly |A| =

∴ |A| = {using trigonometric identity}

Adj(A) is given by the transpose of the cofactor matrix.

∴ adj(A) =

∴ A^-1 =

According to question:

A’ = A^-1

∴

As both the matrices are equal irrespective of the value of α.

∴ α can be any real number …ans