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Matrices & Determinants: Let Square Matrices Non Singular

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

Question

Let

A

and

B

be square matrices such that

AB = 0

and

B

is non-singular. Then:

|A|

must be zero but

A

may be non-zero

A

must be the zero matrixcorrect

Cnothing can be said in general about

A

Dnone of these

Solution

Step 1: Use the non-singularity of

B

Since

B

is non-singular,

B^{-1}

exists. Right-multiply

AB = 0

B^{-1}

A\cdot B\cdot B^{-1} = 0\cdot B^{-1} \implies A\cdot I = 0 \implies A = 0

Therefore

A

must be the zero matrix. Answer: (2)

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