Assertion (A): A 3 × 3 matrix with a row of zeros has no inverse.
Reason (R): The determinant of such a matrix is 0.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

Expanding along the zero row, every term is 0, so the determinant is 0: R is true.
A matrix with determinant 0 is singular and has no inverse, so A is true, and R is the reason.

Concept: Singular and non-singular matrices
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsThe adjoint and the inverse

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Assertion (A): A 3 × 3 matrix with a row of zeros has no inverse.Reason (R): The determinant of such a matrix is 0.

Explanation

Assertion (A): A 3 × 3 matrix with a row of zeros has no inverse.
Reason (R): The determinant of such a matrix is 0.