Assertion (A): If $Δ = |\begin{array}{ccc} 1 & 0 & 1 \\ 1 & - 2 & 3 \\ 5 & 3 & 8 \end{array}|$ , then Δ = −12.
Reason (R): If we expand the determinant either by any row or by any column, then
the value of determinant always be same.

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Both A and R are true and R is the correct explanation of A.

Both A and R are true and R is not the correct explanation of A.

A is true but R is false.

A is False but R is true.

answer is A.

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Detailed Solution

$Given, Δ = |\begin{array}{ccc} 1 & 0 & 1 \\ 1 & - 2 & 3 \\ 5 & 3 & 8 \end{array}|$
$\begin{array}{l} = 1 {- 16 - 9} + 1 {3 + 10} \\ = - 25 + 13 \\ = - 12 [expanding along R_{1}] \end{array}$

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