Question

IF ALL ELEMENTS OF A THIRD ORDER DETERMINANT ARE EQUAL TO 1 OR -1, THEN THE DETERMINANT ITSELF IS
(a) an ODD NUMBER
(b) an EVEN NUMBER
(c)an IMAGINARY NUMBER
(d) a REAL NUMBER

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{A}=\left|\begin{array}{ccc}1& 1& -1\\ 1& -1& 1\\ 1& 1& -1\end{array}\right| \\ =1\left(1-1\right)-1\left(-1-1\right)-1\left(1+1\right) \\ =2-2 \\ =0 \\ \mathrm{So}\mathrm{it}\mathrm{is}\mathrm{always}\mathrm{a}\mathrm{real}\mathrm{number}. \end{gathered}$$