Concept:1). A square matrix A = [aij]n x n, is said to be a scalar matrix if; aij = 0, when i ? j aij = k, when i = j, for some constant k2). Non Singular matrix is a square matrix whose determinant is a non-zero value. 3). Null matrix or zero matrices is a matrix having zero as all its elements.Formula used:\(\displaystyle A^{-1}=\frac{adj\ A}{?\ A ? }\) Calculation:Given that, A is a non-singular matrix and B = adj AWe know that \(\displaystyle A^{-1}=\frac{adj\ A}{?\ A ? }\) ------(i)Statement I: AB = BAPre-multiplication by A,?? \(\displaystyle AA^{-1}=\frac{A.\ adj\ A}{?\ A ? }\)?? \(\displaystyle I=\frac{A.\ adj\ A}{?\ A ? }\)? I ?A? = AB [As B = adj A] ------(ii)Post-multiplication by A,?? \(\displaystyle A^{-1}A=\frac{\ adj\ A.A}{?\ A ? }\)?? \(\displaystyle I=\frac{\ adj\ A.A}{?\ A ? }\)? I ?A? = BA [As B = adj A] ------(iii)From equation (ii) and (iii), we have,AB = BAStatement I is true.Statement II: AB is a scalar matrixFrom equation (ii), we have, AB = ?A? I ? AB is a scalar matrixStatement III: AB can be a null matrixA is a non-singular matrix.??A? ? 0A (adjA) = ?A? I ? 0AB ? 0? Only statement I and Statement II are correct.