Question

For 0 < θ < π, if A = `[(costheta, -sintheta), (sintheta, costheta)]`, then ______ 

Options

• A^T = A

• A^T = -A

• A² = I

• A^T = A^-1 

Answer 1

For 0 < θ < π, if A = `[(costheta, -sintheta), (sintheta, costheta)]`, then A^T = A^-1.

Explanation:

Here, A^T = `[(costheta, sintheta), (-sintheta, costheta)]`

Also, A^-1 = `(AdjA)/|A| =  [(costheta, sintheta), (-sintheta, costheta)]` ...........[∵ |A| = 1]

∴ A^T = A^-1