Determinants Test

Result

Determinants Test - 1

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Question 1
1 / -0

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

A
Det.B=0

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

C
Det.=A =0

D
BA

Solution

Explanation:

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 iff det A is equal to

A
1

B
non zero

C
0

D
–1

Solution

Explanation:

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
none of these

C
|B| = 0AB = O ⇒ |A| = 0

D
AB = O ⇒ |A| = 0 and |B| = 0

Solution

Explanation:

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

A
det B + detC

B
none of these

C
det B

D
det C

Solution

Explanation:

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