Determinants Test

Result

Determinants Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

If A, B be two square matrices such that |AB|=O, then

A
BA

B
Det. A=0 or Det. B =0 or both A and B =0

C
Det.=A =0

D
Det.B=0

Solution

If A B be two square matrices such that AB=O, then, |AB| = O ⇒ |A||B| = O ⇒either |A| = 0 or |B| = 0
Question 2
1 / -0

A square matrix A is invertible if det A is equal to

A
1

B
–1

C
0

D
non zero

Solution

Only non-singular matrices possess inverse
Question 3
1 / -0

If A and B are square matrices of order 3, then

A
adj(AB) = adj A adj B

B
|B| = 0 AB = O |B|=0⇒ |A| = 0

C
AB = O ⇒ |A| = 0 and |B| = 0

D
None of these

Solution

If A B be two square matrices of order 3 and if |B|=0, AB=0 then this is possible only if |A| may be zero
Question 4
1 / -0

If A ,B and C be the three square matrices such that A = B + C, then Det A is equal to

A
det C

B
det B

C
det B + detC

D
None of these

Solution

Because, if A=B+C then |A| = |B+C|