alleryStart learning →A square matrix $A$ is invertible if and only if:
- $A$ is symmetric
- $A$ is of even order
- $|A| = 0$
- $|A| \neq 0$
Show answer and solution
Correct answer: D. $|A| \neq 0$
A is invertible exactly when it is non-singular, i.e. |A| ≠ 0.
Indian Navy AA (Artificer Apprentice) Determinants — practice questions
Explore 27 free Determinants questions in Indian Navy AA (Artificer Apprentice) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Determinants with Quill →Determinants questions and exercises with answers
Showing questions 1–27 of 27.
A square matrix $A$ is invertible if and only if:Read the answer and worked solution →The value of the determinant $\begin{vmatrix} 2 & 4 \\ 3 & 5 \end{vmatrix}$ is:Read the answer and worked solution →Singular or non-singular?Read the answer and worked solution →Match each term to its definitionRead the answer and worked solution →Minors and cofactorsRead the answer and worked solution →True or false: cofactor expansionRead the answer and worked solution →Order the steps for finding A⁻¹Read the answer and worked solution →Determinant of a 2 × 2 matrixRead the answer and worked solution →Complete the inverse ruleRead the answer and worked solution →True or false: adjoint and inverseRead the answer and worked solution →Assertion and reason: invertibilityRead the answer and worked solution →Tap every statement that is true of a non-singular matrixRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Flip and pair: symbol with meaningRead the answer and worked solution →Complete the area formulaRead the answer and worked solution →Adjoint and identityRead the answer and worked solution →Order the steps for the area of a triangleRead the answer and worked solution →Which side of the inverse test?Read the answer and worked solution →True or false: expanding a determinantRead the answer and worked solution →Match each condition to what it tells youRead the answer and worked solution →Assertion and reason: cofactorsRead the answer and worked solution →Spot the odd oneRead the answer and worked solution →Tap everything the chapter actually definesRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Two true, one false: scope of the chapterRead the answer and worked solution →
Worked practice questions
The value of the determinant $\begin{vmatrix} 2 & 4 \\ 3 & 5 \end{vmatrix}$ is:
- $2$
- $22$
- $-22$
- $-2$
Show answer and solution
Correct answer: D. $-2$
Determinant = (2)(5) − (4)(3) = 10 − 12 = −2.
Singular or non-singular?
Read exercise and reference answers
- Items
- Item
- |A| = 0
- Category
- Singular
- Item
- |A| = −7
- Category
- Non-singular
- Item
- A has no inverse
- Category
- Singular
- Item
- A⁻¹ exists
- Category
- Non-singular
- Item
- |A| = 1
- Category
- Non-singular
- Item
- A(adj A) = O
- Category
- Singular
- Categories
- Item
- Singular
- Item
- Non-singular
Your syllabus defines a square matrix as singular when |A| = 0 and non-singular when |A| ≠ 0. The whole inverse story hangs on which side a matrix falls. Source: syllabus Maths Part I, Ch 4 Determinants.
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