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in Matrices & determinants by (418 points)


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Correct option is (A) \(\frac1{5^3}+\frac1{5^6}-\frac1{5^9}\)

Total no. of matrices of order 3 x 3 formed by using the elements of the set 

A = {-2, -1, 0, 1, 2} = 59

(\(\because\) There are total 9 elements in the matrix and each element have 5 choices)

Total no. of symmetric matrices formed by Set A = {-2, -1, 0, 1, 2} = 56

Total no. of skew symmetric matrices formed by Set A = 53

Total no. of matrices which is both symmetric and skew symmetric formed by using elements of Set A = 1

(\(\because\) only zero matrix is both symmetric & skew symmetric.)

\(\therefore\) Total no. of matrices that is either symmetric or skew symmetric and formed by elements of Set A = Total no. of symmetric matrices  + Total no. of skew symmetric matrices - Total no. of matrices which are both 

 = 56 + 53 - 1

\(\therefore\) required probability = \(\frac{5^6+5^3-1}{5^9}\) = \(\frac1{5^3}+\frac1{5^6}-\frac1{5^9}\)

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