Question

If B(adj B) = [[1/3, 0, 0], [0, 1/3, 0], [0, 0, 1/3]], then the value of det(B⁻¹) =

If A is a non-singular matrix, then which of the following is not true ?

If A = [[3, 2],[7, 5]], B = [[6, 7],[8, 9]], then show that (AB)⁻¹ = B⁻¹A⁻¹.

If A is a 3×3 invertible matrix, show that for any scalar k ≠ 0, (kA)⁻¹ = (1/k)A⁻¹. Hence calculate (3A)⁻¹, where A = [[2,-1,1],[-1,2,-1],[1,-1,2]]