Gate 2019

Question

What is the for the question where two statements were given as:

S1: matrix A is invertible

S2:|A|=0?

Comments

Is it not only s1 implies s2?

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s1 implies s2 and also s2 implies s1

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S2 was |A| Does not equal to zero and answer was Both are equivalent

Answer 1

Both are equivalent

Answer 2

Both are equal .

S1: Matrix is invertible , meaning determinant exists and is non zero  , therefore S1 implies S2.

S2: Determinant of the matrix is non zero , meaning inverse of the matrix is possible making S2 implies S1 .

And  When both the statements can imply each other we can say for sure that they are equivalent to each other.

Comments

Both are equivalent