Question

The value of the determinant
$\left|\begin{array}{c}1\\ {}^m{C}_1\\ {}^m{C}_{21}\end{array}\begin{array}{c}1\\ {}^{m+1}{C}_1\\ {}^{m+1}{C}_2\end{array}\begin{array}{c}1\\ {}^{m+2}{C}_1\\ {}^{m+2}{C}_2\end{array}\right|$ is equal to

• A. $1$
• B. $-1$
• C. $0$
• D. None of these

Answer 1

The correct option is A $1$

There are some properties to find the determinant without expanding them, they are :

$\Rightarrow$ If a matrix has all the elements zero in any row or column, then value of its determinant is zero

$\Rightarrow$ If a matrix has any two rows or columns identical, then the value of its determinant is zero

$\Rightarrow$ by substituting $C1=C1+C2+C3$ if it gives the C1 as 0 then the value of its determinant is zero.

here these three points are not satisfied hence the determinant is $1$