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Let $M = {[\begin{array}{l} a & b \\ c & d \end{array}] : a, b, c, d \in ℝ ($ set of all real numbers $)}$ and $I = [\begin{array}{l} 1 & 0 \\ 0 & 1 \end{array}]$
If $A \in M, tr (A) = x, \det (A) = y$ then

COLUMN - I
COLUMN – II
1 Value of $\det (A + I) =$ , when x = 2, y = 3 P 1
2 Value of $\det (A - I) =$ , when x = 2, y = 3 Q 2
3 Value of $\det (A - I) =$ , when x = 3, y = 2 R 6
4 Value of $\det (A + I) =$ , when x = 3, y = 2 S 0

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1 - R, 2 - Q, 3 - S, 4 - R

1 - Q, 2 - S, 3 - Q, 4 - R

1 - Q, 2 - S, 3 - R, 4 - Q

1 - R, 2 - S, 3 - Q , 4 - Q

answer is A.

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Detailed Solution

$\det (A + I) = x + y + 1, \det (A - I) = 1$

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