JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q3

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MathematicsSingle correct+4 / -1Question 3 of 90

Let A and B be two 3 × 3 non-zero real matrices such that AB is a zero matrix. Then

the system of linear equations AX = 0 has a unique solution

the system of linear equations AX = 0 has infinitely many solutions

B is an invertible matrix

adj(A) is an invertible matrix

Answer and worked solution

Official answer: B

Singular A. B has a non-zero column $X$ with $AX=0$ , so A is singular and $AX=0$ has infinitely many solutions. Likewise B is singular (else $A=0$ ), and adj A of a singular 3 × 3 matrix is singular.

(B)

Topics:Systems of linear equations Adjoint and inverse

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JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 3