Question

Which of the following is not correct?

पर्याय

• \[|A| = | A^T |,\text{ where }A = \left[ a_{ij} \right]_{3 \times 3}\] 

• \[|kA| = | k^3 |,\text{ where }A = \left[ a_{ij} \right]_{3 \times 3}\]

• If A is a skew-symmetric matrix of odd order, then |A| = 0

• \[\begin{vmatrix}a + b & c + d \\ e + f & g + h\end{vmatrix} = \begin{vmatrix}a & c \\ e & g\end{vmatrix} + \begin{vmatrix}b & d \\ f & h\end{vmatrix}\]

Answer 1

(d) \[\begin{vmatrix}a + b & c + d \\ e + f & g + h\end{vmatrix} = \begin{vmatrix}a & c \\ e & g\end{vmatrix} + \begin{vmatrix}b & d \\ f & h\end{vmatrix}\]

\[\begin{vmatrix} a + b & c + d\\e + f & g + h \end{vmatrix} = \begin{vmatrix} a + b & c\\e + f & g \end{vmatrix} + \begin{vmatrix} a + b & d\\e + f & h \end{vmatrix}\]
\[ = \begin{vmatrix} a & c\\e & g \end{vmatrix} + \begin{vmatrix} b & c\\f & g \end{vmatrix} + \begin{vmatrix} a & d \\e & h \end{vmatrix} + \begin{vmatrix} b & d\\f & h \end{vmatrix}\]