Question # 1

If each element of a 3 × 3 matrix A is multiplied by 3, then the determinant of the resulting matrix is:

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|A|³

27|A|

3|A|

9|A|

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1

-5

-1

none

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singular

non-singular

rectangular

null

If two rows (or two columns) in a square matrix are identical (i.e. corresponding elements are equal), the value of the determinant is:

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0

1

-1

±1

If A is a square matrix order 3 × 3 the |kA| equals:

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k |A|

k²|A|

k³ |A|

k⁴ |A|

A^-1 exists if A is:

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singular

nonsingular

symmetric

none

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scalar matrix

diagonalmatrix

triangularmatrix

none of these

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For a square matrix A, |A| equals:

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A^t

|A^t|

-|A^t|

-A^t

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ab - cd = 0

ac - bd = 0

ad - bc = 1

ad - bc = 0

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diagonal matrix

[0] is a:

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If A = [a_ij], B = [b_ij] and AB = 0 then:

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A = 0

B = 0

either A = 0 or B = 0

A & B not necessarily zero

If any two rows of a square matrix are interchanged, the determinant of the resulting matrix:

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is zero

is multiplicative inverse of the determinant of the original matrix

is additive inverse of the determinant the original matrix

none of these

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5

-5

-4

4

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None

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5

14

20

6

If A is non singular matrix then A^t is:

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singular

nonsingular

symmetric

none

A matrix in which each element is 0 is called:

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If A is a square matrix, then:

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|A^t| = A

|A^t| = -A

|A^t| = |A|

A^t= A

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