Let be a invertible matrix with real entries and let denote the identity matrix

MATHEMATICS · Single correct · CBSE · Mathematics · Matrices · Matrices

Problem

Let

M

be a

3 \times 3

invertible matrix with real entries and let

I

denote the

3 \times 3

identity matrix. If

M^{-1} = \text{adj}(M)

, then which of the following statements is/are ALWAYS TRUE? (A)

M = I

(B)

\det M = 1

. (C)

M^2 = I

(D)

(\text{adj } M)^2 = I