Let A be a 2 × 2 real matrix with entries from 0 , 1 and A ≠ 0 . Consider the following two statements; P If A ≠ l 2 , then A = - 1 Q If A = 1 , then t r A = 2 Where l 2 denotes 2 × 2 identity matrix and t r A denotes

Question

Let A be a 2 &#215; 2 real matrix with entries from 0 , 1 and A &#8800; 0 . Consider the following two statements; P If A &#8800; l 2 , then A = - 1 Q If A = 1 , then t r A = 2 Where l 2 denotes 2 &#215; 2 identity matrix and t r A denotes the sum of the diagonal entries of A . Then

Quantrex Academy · Accepted Answer

Correct answer: D. Both P and Q are true

Let A = a b c d &#160;&#160; a , b , c , d &#8712; 0 , 1 A = a d - b c &#8800; 0 &#8658; &#160; a d = 1 , b c = 0 or a d = 0 , b c = 1 P If A &#8800; I 2 &#8658; a d &#8800; 1 &#8658; a d = 0 , b c = 1 &#8658; | A | = - 1 P is true. Q If A = 1 &#8658; a d = 1 , b c = 0 &#8658; &#160; tr ( A ) = 2 Q is true.

Let A be a 2 × 2 real matrix with entries from 0 , 1 and A ≠ 0 . Consider the following two statements; P If A ≠ l 2 , then A = - 1 Q If A = 1 , then t r A = 2 Where l 2 denotes 2 × 2 identity matrix and t r A denotes the sum of the diagonal entries of A . Then

Options

Correct answer

Step-by-step solution

More from Matrices

Let A be a 2 &#215; 2 real matrix with entries from 0 , 1 and A &#8800; 0 . Consider the following two statements; P If A &#8800; l 2 , then A = - 1 Q If A = 1 , then t r A = 2 Where l 2 denotes 2 &#215; 2 identity matrix and t r A denotes the sum of the diagonal entries of A . Then

Options

Correct answer

Step-by-step solution

More from Matrices

Let A be a 2 × 2 real matrix with entries from 0 , 1 and A ≠ 0 . Consider the following two statements; P If A ≠ l 2 , then A = - 1 Q If A = 1 , then t r A = 2 Where l 2 denotes 2 × 2 identity matrix and t r A denotes the sum of the diagonal entries of A . Then