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1
JEE Main 2021 (Online) 20th July Evening Shift
Numerical
+4
-1
Let $$A = \{ {a_{ij}}\}$$ be a 3 $$\times$$ 3 matrix,

where $${a_{ij}} = \left\{ {\matrix{ {{{( - 1)}^{j - i}}} & {if} & {i < j,} \cr 2 & {if} & {i = j,} \cr {{{( - 1)}^{i + j}}} & {if} & {i > j} \cr } } \right.$$

then $$\det (3Adj(2{A^{ - 1}}))$$ is equal to _____________.
2
JEE Main 2021 (Online) 20th July Morning Shift
Numerical
+4
-1
Let $$A = \left( {\matrix{ 1 & { - 1} & 0 \cr 0 & 1 & { - 1} \cr 0 & 0 & 1 \cr } } \right)$$ and B = 7A20 $$-$$ 20A7 + 2I, where I is an identity matrix of order 3 $$\times$$ 3. If B = [bij], then b13is equal to _____________.
3
JEE Main 2021 (Online) 20th July Morning Shift
Numerical
+4
-1
Let a, b, c, d in arithmetic progression with common difference $$\lambda$$. If $$\left| {\matrix{ {x + a - c} & {x + b} & {x + a} \cr {x - 1} & {x + c} & {x + b} \cr {x - b + d} & {x + d} & {x + c} \cr } } \right| = 2$$, then value of $$\lambda$$2 is equal to ________________.
Let I be an identity matrix of order 2 $$\times$$ 2 and P = $$\left[ {\matrix{ 2 & { - 1} \cr 5 & { - 3} \cr } } \right]$$. Then the value of n$$\in$$N for which Pn = 5I $$-$$ 8P is equal to ____________.