Question

Find the cofactor of the element $a_{32}$ in the matrix $\left[\begin{array}{ccc}5& 1& 2\\ 3& 2& 1\\ 9& 9& 5\end{array}\right]$

• A. -1
• B. +1
• C. 0
• D. -2

Answer 1

The correct option is B

+1

You know cofactor is given by the formula.

$A_{ij}=(-1{)}^{i+j}.M_{ij}$

Where $M_{ij}$ is the minor of the element $a_{ij}$

Also minor of an element is simply the determinant of the submatrix obtained by removing the column and rows of that element from the original matrix. Removing the third row and second column and taking the determinant we get,

$M_{32}$ = $\left|\begin{array}{cc}5& 2\\ 3& 1\end{array}\right|=5-6=-1$

$Cofactor{A}_{32}=(-1{)}^{3+2}.M_{32}=-1.-1=+1$