More than one correct Answer IIT JEE 2011 Let M and N be two 3 x 3 non-singular skew-symmetric matrices such that MN NM. If P denotes the transpose of P, then N2(MTN)-1 (MN-1) is equal to (a) M2 (d) MN Given, MT - And M N = N M 1T 2 M2N(1)(-M)-1(-N)-1 (-M)

IIT JEE 2009 Let A be the set of all 3 x 3 symmetric matrices all of whose entries are 0 either 1 such that five of these entries are 1 and four are zero. The number of matrices in set A, is (a) 12 (b) 6 (c) 9 (d) 3 4 zero 5 one A symmetric matrix is symmetric about its diagonal. So, there are even number of 1 and even number of 0 as of diagonal entries. Consequently, there can be either three 1 in the diagonal or one 1 and two zeros. Thus, we have the following cases: Case 1: When the diagonal elements are 1, 1,1 In this case, we have Number of symmetric matricesNumber of arrangements of 1, 0, 0 as elements above the diagonal 3!

IIT JEE 2009 Let A be the set of all 3 x 3 symmetric matrices all of whose entries are 0 either 1 such that five of these entries are 1 and four are zero. The number of matrices in set A, is (a) 12 (b) 6 (c) 9 (d) 3 4 zero 5 one Case 2: When diagonals elements are 1,0,0 In this case, we have Number of symmetric matrices -(Number of arrangements of 1, 0, 0 in diagonal) x (Number of arrangements of 1,1,0 as entries above the diagonal) 3! 3! 0 Total number of matrices 3 +9 12

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Swapandeep Satyam

4 months ago

Thank you Sir for the video

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Kashif Iqbal

7 months ago

Fabulous questions sir👌👌👌👌

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Tushar Goyal

a year ago

awesome

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