GATE | GATE CS 1997 | Question 27

Let A= (a_ij) be an n-rowed square matrix and I₁₂ be the matrix obtained by interchanging the first and second rows of the n-rowed Identify matrix. Then AI₁₂ is such that its first (A) row is the same as its second row (B) row is the same as the second row of A (C) column is the same as the second column of A (D) row is all zero
Answer:(C)
Explanation: When the above matrices are multiplied, the result is , which is the matrix A with it’s first and second row interchanged. This is because the first row of has a 1 in the second column and it’s second row has a 1 in the first column. So when the matrices are multiplied, the first and second rows get exchanged. This explanation is provided by Chirag Manwani.
Quiz of this Question