Concept:1). Transpose of a Matrix: The new matrix obtained by interchanging the rows and columns of the original matrix is called the transpose of the matrix. For example: \(A = \begin{bmatrix} a &b & c \\[0.3em] x & y & z \\[0.3em] \end{bmatrix}\)? \(A^T = \begin{bmatrix} a &x \\[0.3em] b & y \\[0.3em] c & z \\[0.3em] \end{bmatrix}\) It is denoted by A' or AT.2). For the addition and subtraction of two matrices, the order of matrices should be equal.Calculation:Given:\(A = \begin{bmatrix} 1 &0 & 0 \\[0.3em] 0& 1 &0\\[0.3em] 0 & 0 & 1 \end{bmatrix}\)and \(B = A^T= \begin{bmatrix} 1 &0 & 0 \\[0.3em] 0& 1 &0\\[0.3em] 0 & 0 & 1 \end{bmatrix}\)C = A + B? \(C = \begin{bmatrix} 1 &0 & 0 \\[0.3em] 0& 1 &0\\[0.3em] 0 & 0 & 1 \end{bmatrix}+ \begin{bmatrix} 1 &0 & 0 \\[0.3em] 0& 1 &0\\[0.3em] 0 & 0 & 1 \end{bmatrix}\)? \(C = \begin{bmatrix} 2 &0 & 0 \\[0.3em] 0& 2 &0\\[0.3em] 0 & 0 & 2 \end{bmatrix}\)? ?C? = 2(4 - 0)? ?C? = 8? The determinant of matrix C is 8.