Chapter 4 Determinants Ex 4.2 Solutions
Question - 11 : - By using properties ofdeterminants, show that-
Answer - 11 : -
(i) 
(ii) 
Solution
(i) 
Applying R1 → R1 + R2 + R3, we have:
Applying C2 → C2 − C1, C3 → C3 − C1, we have:
Expanding along C3, we have:
Hence, the given resultis proved.
(ii) 
Applying C1 → C1 + C2 + C3, we have:
Applying R2 → R2 − R1 andR3 → R3 − R1, we have:
Expanding along R3, we have:
Hence, the given resultis proved.
Question - 12 : - By using properties ofdeterminants, show that:
Answer - 12 : -
Applying R1 → R1 + R2 + R3, we have:
Applying C2 → C2 − C1 andC3 → C3 − C1, we have:
Expanding along R1, we have:
Hence, the given resultis proved.
By using properties ofdeterminants, show that:
Answer - 13 : -
Applying R1 → R1 + bR3 and R2 → R2 − aR3, we have:
Expanding along R1, we have:
By using properties ofdeterminants, show that:
Answer - 14 : -
Taking out commonfactors a, b, and c from R1, R2, and R3 respectively,we have:
Applying R2 → R2 − R1 andR3 → R3 − R1, we have:
Applying C1 → aC1, C2 → bC2, andC3 → cC3, we have:
Expanding along R3, we have:
Hence, the given resultis proved.
Choose the correctanswer.
Let A bea square matrix of order 3 × 3, then 
is equal to
Answer - 15 : -
A.
B. 
C. 
D. 
Solution
A is a square matrix of order 3 × 3.
Hence, the correctanswer is C.
Question - 16 : - Which of the followingis correct?
Answer - 16 : -
A. Determinant is a square matrix.
B. Determinant is a number associated to amatrix.
C. Determinant is a number associated to asquare matrix.
D. None of these
Solution
We know that to everysquare matrix, 
of order n. We canassociate a number called the determinant of square matrix A,where 
element of A.
Thus, the determinant isa number associated to a square matrix.
Hence, the correctanswer is C.