Q64 / 150 · MHT CET 2019 (Shift 1) · Mathematics

If A and B are square matrices of order 3 such that $|A| = 2, |B| = 4,$ then $|A (a d j B)| =$ …

A
16
B
8
C
64
Correct answer
D
32

Solution

We have, A and B are square matrices of order 3 such that

|A| = 2, |B| = 4

Now,

|A (a d j) B| = |A| |a d j B| (∵ |A B| = |A| |B|)

|A| {|B|}^{3 - 1}

= |A| {|B|}^{2} = (2) {(4)}^{2} = 32

Hence, the correct answer is option: 'D'.

More Determinants Questions

Let and , where denotes the cofactor of an element of matrix , then the value of is :20 Apr, 2026 (E)Expansion of Determinants
If then the distance of point from the plane is11 Apr, 2026 (E)System of Linear Equations
The lines are concurrent then are in22 Apr, 2025 (E)Expansion of Determinants
If , then the value of20 Apr, 2025 (E)System of Linear Equations
If \([2 { {p}}-3 { {r}} ~ { {q}} ~ { {s}}]+[3 { {p}}+2 { {q}} ~ { {r}} ~ { {s}}]= {m}[ { {p}} ~ { {r}} ~ { {s}}]+ {n}[ { {q}} ~ { {r}} ~ { {19 Apr, 2025 (M)Expansion of Determinants
If , where are cofactors of respectively, then the value of19 Apr, 2025 (M)Expansion of Determinants