Question

Using the elements $-3,-2,-1,0,1,2,3$ the matrices of order $3 \times 3$ formed then

• A. The number of matrices having trace 0 is $37\left(7^6\right)$
• B. If one matrix out of all the matrices formed is chosen randomly then the probability that it is symmetric is $\frac{1}{343}$
• C. The number of skew symmetric matrices is $7^3$
• D. The number of symmetric matrices is $7^6$

Answer 1

Answer: (A), (B), (C), (D)

Correct answer is (a) The number of matrices having trace 0 is $37\left(7^6\right)$Correct answer is (b) If one matrix out of all the matrices formed is chosen randomly then the probability that it is symmetric is $\frac{1}{343}$Correct answer is (c) The number of skew symmetric matrices is $7^3$Correct answer is (d) The number of symmetric matrices is $7^6$