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

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MathematicsMatricesProduct of MatricesEasy2 minPYQ_2022

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Let $A$ and $B$ be two $3 \times 3$ non-zero real matrices such that $A B$ is a zero matrix. Then

Question diagram: Let A and B be two 3 × 3 non-zero real matrices such that A

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Solution:

Given,
$A B = 0 \Rightarrow |A B| = 0$
If $|A| \neq 0, B = 0$ (not possible)
If $|B| \neq 0, A = 0$ (not possible)
Hence $|A| = |B| = 0$
So, if $|A| = |B| = 0$ then $A & B$ are non-invertible matrix,
So, AX=0 has infinitely many solutions

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:Product of Matrices

⏱ 2mℹ️ Source: PYQ_2022

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