Let A = (aᵢⱼ) be an n-rowed square matrix and I₁₂ be the matrix obtained by…
1997
Let A = (aᵢⱼ) be an n-rowed square matrix and I₁₂ be the matrix obtained by interchanging the first and second rows of the n-rowed identity matrix. Then A I₁₂ 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
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Correct answer: C
I₁₂ is obtained by interchanging the first two rows of the identity matrix. When a matrix A is multiplied on the right by this permutation matrix, the corresponding columns of A are interchanged. Therefore, in A I₁₂, the first column becomes the second column of A (and the second column becomes the first column of A). Hence the first column of A I₁₂ is the same as the second column of A.