Question

Two nonzero distinct numbers $a,b$ are used as elements to make determinants of the third order. The number of determinants whose value is zero for all $a,b$ are

• A. $24$
• B. $32$
• C. $a+b$
• D. none of these

Answer 1

Answer: (B)

$32$

For $det=0$

Atleast two rows are same

Firstly

Total no. of possible determinants$=?$

Each element in a row$-2$ choices

$3$ rows-$2\times 2\times 2=8$

There are $3$ columns-$8\times 8\times 8=512$

Total determinants$=512$

No. of matrices with no row or column same${=}^8{C}_3{\times }^3{P}_3=336$

Required Answer$=512-336=176$