Let A be a 2 × 2 matrix of the form A = a b 1 1 , where a ,   b are integers and - 50 ≤ b ≤ 50 . The number of such matrices A such that A - 1 , the inverse of A , exists and A - 1 contains only integer entries is

Question

Let A be a 2 &#215; 2 matrix of the form A = a b 1 1 , where a , &#160; b are integers and - 50 &#8804; b &#8804; 50 . The number of such matrices A such that A - 1 , the inverse of A , exists and A - 1 contains only integer entries is

Quantrex Academy · Accepted Answer

Correct answer: C. 202

&#8800; 0 &#8658; a - b &#8800; 0 &#8658; a &#8800; b . . . ( i ) Also, A &#8722; 1 = 1 a &#8722; b 1 &#8722; 1 &#8722; b a T = 1 a &#8722; b 1 &#8722; b &#8722; 1 a Thus, a - b = 1 or - 1 . . . ii So, required number of pairs ( a , &#160; b ) is 101 &#215; 2 = 202

Let A be a 2 × 2 matrix of the form A = a b 1 1 , where a ,   b are integers and - 50 ≤ b ≤ 50 . The number of such matrices A such that A - 1 , the inverse of A , exists and A - 1 contains only integer entries is

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Correct answer

Step-by-step solution

More from Matrices

Let A be a 2 &#215; 2 matrix of the form A = a b 1 1 , where a , &#160; b are integers and - 50 &#8804; b &#8804; 50 . The number of such matrices A such that A - 1 , the inverse of A , exists and A - 1 contains only integer entries is

Options

Correct answer

Step-by-step solution

More from Matrices

Let A be a 2 × 2 matrix of the form A = a b 1 1 , where a , b are integers and - 50 ≤ b ≤ 50 . The number of such matrices A such that A - 1 , the inverse of A , exists and A - 1 contains only integer entries is