Let A = bmatrix 0 & -2 2 & 0 bmatrix . If M and N are two matrices given by M = _ k=1 ^ 10 A^ 2k and N = _ k=1 ^ 10 A^ 2k-1 then MN^ 2 is :

JEE Main 2022 Mathematics question

Let . If M and N are two matrices given by and then is :

Answer: (1)

= −4I. So + … + = −4I + 16I − 64I + … (10 terms), a G.P. in (−4) that sums to , a scalar multiple of the identity. + … + $ = A(1 - 4

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Question ID VK-024994