jee-advanced 2014 Q50

jee-advanced · India · paper1 Matrices Structured Matrix Characterization

Let $M$ be a $2 \times 2$ symmetric matrix with integer entries. Then $M$ is invertible if
(A) the first column of $M$ is the transpose of the second row of $M$
(B) the second row of $M$ is the transpose of the first column of $M$
(C) $M$ is a diagonal matrix with nonzero entries in the main diagonal
(D) the product of entries in the main diagonal of $M$ is not the square of an integer

Let $M$ be a $2 \times 2$ symmetric matrix with integer entries. Then $M$ is invertible if\\
(A) the first column of $M$ is the transpose of the second row of $M$\\
(B) the second row of $M$ is the transpose of the first column of $M$\\
(C) $M$ is a diagonal matrix with nonzero entries in the main diagonal\\
(D) the product of entries in the main diagonal of $M$ is not the square of an integer

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