Let A = a i j 1 ≤ i , j ¯ 3 be a 3 × 3 invertible matrix where each a i i is a real number. Denote the inverse of the matrix A by A - 1 . If ∑ i t l 3 a i j = 1 for 1 ≤ i ≤ 3 , then

Question

Let A = a i j 1 &#8804; i , j &#175; 3 be a 3 &#215; 3 invertible matrix where each a i i is a real number. Denote the inverse of the matrix A by A - 1 . If &#8721; i t l 3 a i j = 1 for 1 &#8804; i &#8804; 3 , then

Quantrex Academy · Accepted Answer

Correct answer: B. sum of each row of A - 1 is 1

Sum of elements in each row of A is 1 . So, A 1 1 1 = 1 1 1 &#8658; A - 1 &#160; A 1 1 1 = A - 1 1 1 1 &#8658; 1 1 1 = A - 1 1 1 1 &#8658; sum of elements in each row of A - 1 is 1

Let A = a i j 1 ≤ i , j ¯ 3 be a 3 × 3 invertible matrix where each a i i is a real number. Denote the inverse of the matrix A by A - 1 . If ∑ i t l 3 a i j = 1 for 1 ≤ i ≤ 3 , then

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More from Matrices

Let A = a i j 1 &#8804; i , j &#175; 3 be a 3 &#215; 3 invertible matrix where each a i i is a real number. Denote the inverse of the matrix A by A - 1 . If &#8721; i t l 3 a i j = 1 for 1 &#8804; i &#8804; 3 , then

Options

Correct answer

Step-by-step solution

More from Matrices

Let A = a i j 1 ≤ i , j ¯ 3 be a 3 × 3 invertible matrix where each a i i is a real number. Denote the inverse of the matrix A by A - 1 . If ∑ i t l 3 a i j = 1 for 1 ≤ i ≤ 3 , then