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 INET Determinants — practice questions
Explore 27 free Determinants questions in Indian Navy INET 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 →If $A$ and $B$ are $3\times3$ matrices with $|A| = 2$ and $|B| = 3$, then $|AB|$ equals: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
If $A$ and $B$ are $3\times3$ matrices with $|A| = 2$ and $|B| = 3$, then $|AB|$ equals:
- 5
- 8
- 36
- 6
Show answer and solution
Correct answer: D. 6
|AB| = |A|·|B| = 2·3 = 6.
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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