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A matrix A is invertible if it has all zeroes in one or more rows on L.H.S.

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in Mathematics - Class 12 by (687k points)
A matrix A is invertible if it has all zeroes in one or more rows on L.H.S.

(a) True

(b) False

This question was addressed to me in an online quiz.

My doubt stems from Invertible Matrices in chapter Matrices of Mathematics – Class 12

1 Answer

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Best answer
Right choice is (b) False

To elaborate: The given statement is false. A matrix is non-invertible if it has all zeroes in one or more rows on L.H.S. This is because after applying all the elementary operations on the matrix, we should get an identity matrix on the L.H.S. to obtain an inverse of the given matrix, which is not possible if we obtain all zeroes in one or more rows.

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