Concept:1). For the addition and subtraction of two matrices, the order of matrices should be equal.2). For the multiplication of two matrices, the number of columns in the first matrix should be equal to the number of rows in the first matrix.3). In the multiplication of two matrices, the order of the resultant matrix is such that the number of rows is equal to the first matrix, and the number of columns is equal to the second matrix.Calculation:Given:\(A = [m \ n], B = [-n \ -m] \text{and} \ C = \begin{bmatrix} m \\ -m\end{bmatrix}\)Statement I: CA = CBCA = \(\displaystyle \begin{bmatrix} m \\ -m\end{bmatrix} [m \ n ]\) = \(\begin{bmatrix} m^2 &mn \\[0.3em] -m^2 & -mn\\[0.3em] \end{bmatrix}\)CB = \(\displaystyle \begin{bmatrix} m \\ -m\end{bmatrix} [-n \ -m ]\) = \(\begin{bmatrix} -mn &-m^2 \\[0.3em] mn & m^2\\[0.3em] \end{bmatrix}\)CA ? CBStatement I is incorrect.Statement II: AC = BCAC = \(\displaystyle [m \ n ] \begin{bmatrix} m \\ -m\end{bmatrix}\) = m2 - mnBC = \(\displaystyle [-n \ -m ]\begin{bmatrix} m \\ -m\end{bmatrix}\) = m2 - mnStatement II is correct.Statement III: C(A + B) = CA + CBC(A + B) = \(\displaystyle \begin{bmatrix} m \\ -m\end{bmatrix} ([m\ \ \ n ]+[-n \ -m ])\) = \(\displaystyle \begin{bmatrix} m \\ -m\end{bmatrix} [m-n \ \ \ n-m ]\) = \(\begin{bmatrix} m^2-mn &mn-m^2 \\[0.3em] -m^2+mn & -mn+m^2\\[0.3em] \end{bmatrix}\)CA + CB = \(\begin{bmatrix} m^2 &mn \\[0.3em] -m^2 & -mn\\[0.3em] \end{bmatrix}\) + \(\begin{bmatrix} -mn &-m^2 \\[0.3em] mn & m^2\\[0.3em] \end{bmatrix}\) = \(\begin{bmatrix} m^2-mn &mn-m^2 \\[0.3em] -m^2+mn & -mn+m^2\\[0.3em] \end{bmatrix}\)Statement III is correct.? Both Statement II and Statement III are correct.