If there are 3 square matrix A, B, C of same order satisfying the equation A^2=A⁻¹ . and let B=A^ 2^n and C=A^ (3-3) then det (B-C) is equal to

Step-by-step solution

aligned & B=A^ 2^n = (A^2 )^ 2^ n-1 = (A⁻¹ )^ 2^ n-1 = (A^ 22^ n-2 )⁻¹= (A^2 )^ -2^ n-2 = (A⁻¹ )^ -2^ n-2 =A^ 2^n: & B=C & det (B-C)=0 aligned