Matrices & DeterminantsmediumFree

Matrices & Determinants: Let Square Matrices Non Singular

JEE Maths question with a full step-by-step solution.

Question
Let AA and BB be square matrices such that AB=0AB = 0 and BB is non-singular. Then:
A∣A∣|A| must be zero but AA may be non-zero
BAA must be the zero matrixcorrect
Cnothing can be said in general about AA
Dnone of these
Solution
Step 1: Use the non-singularity of BB Since BB is non-singular, B−1B^{-1} exists. Right-multiply AB=0AB = 0 by B−1B^{-1}:
A⋅B⋅B−1=0⋅B−1  ⟹  A⋅I=0  ⟹  A=0A\cdot B\cdot B^{-1} = 0\cdot B^{-1} \implies A\cdot I = 0 \implies A = 0
 Therefore AA must be the zero matrix. Answer: (2)
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Matrices & Determinants · easy
If A is a 3 × 3 matrix and det A = 5 , then det ( Adj ( Adj ,A) ) equals:
Matrices & Determinants · easy
The equation pmatrix 1 2 2 1 3 4 3 4 k pmatrix pmatrix x y z pmatrix = pmatrix 0 0 0 pmat…
Matrices & Determinants · easy
A is an involutory matrix given by A = pmatrix 0 1 -1 4 -3 4 3 -3 4 pmatrix , then the in…
Matrices & Determinants · easy
A square matrix P satisfies P² = I - P , where I is the identity matrix. If P^n = 5I - 8P…

Solve more, learn faster

Sign up free to solve more JEE Mathsquestions and explore doMath — timed drills, mastery sprints, bookmarks, and chapter-wise progress tracking.

Sign up freeExplore doMath