Let A and B are 3 × 3 matrices with real number entries, where A is symmetric, B is skew-symmetric and A + B A - B = A - B A + B . If A B T = - 1 k A B , then the sum of all possible integral value of k in 2 , 10 is equal to (where A T

Question

Let A and B are 3 &#215; 3 matrices with real number entries, where A is symmetric, B is skew-symmetric and A + B A - B = A - B A + B . If A B T = - 1 k A B , then the sum of all possible integral value of k in 2 , 10 is equal to (where A T represent transpose of matrix A )

Quantrex Academy · Accepted Answer

Correct answer: B. 24

A T = A , B T = - B A + B A - B = A - B A + B ⇒ A 2 - A B + B A - B 2 = A 2 + A B - B A - B 2 ⇒ A B = B A … … i Now, A B T = B T A T = - B A = - A B = - 1 k A B ⇒ k is an odd number ⇒ k = 3 , 5,7 , 9 Sum = 24

Let A and B are 3 × 3 matrices with real number entries, where A is symmetric, B is skew-symmetric and A + B A - B = A - B A + B . If A B T = - 1 k A B , then the sum of all possible integral value of k in 2 , 10 is equal to (where A T represent transpose of matrix A )

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Correct answer

Step-by-step solution

More from Matrices

Let A and B are 3 &#215; 3 matrices with real number entries, where A is symmetric, B is skew-symmetric and A + B A - B = A - B A + B . If A B T = - 1 k A B , then the sum of all possible integral value of k in 2 , 10 is equal to (where A T represent transpose of matrix A )

Options

Correct answer

Step-by-step solution

More from Matrices

Let A and B are 3 × 3 matrices with real number entries, where A is symmetric, B is skew-symmetric and A + B A - B = A - B A + B . If A B T = - 1 k A B , then the sum of all possible integral value of k in 2 , 10 is equal to (where A T represent transpose of matrix A )