A and B are matricesShow by an example that for A ≠ O and B ≠ O, AB = O.

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Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

A and B are matrices

Show by an example that for A ≠ O and B ≠ O, AB = O.

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Let $A = [\begin{array}{cc} 0 & 1 \\ 0 & 1 \end{array}]$ and $B = [\begin{array}{cc} 1 & 1 \\ 0 & 0 \end{array}]$

Clearly, A ≠ O and B ≠ O.

Now,

AB = [\begin{array}{cc} 0 & 1 \\ 0 & 1 \end{array}] [\begin{array}{cc} 1 & 1 \\ 0 & 0 \end{array}] = [\begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array}] = O

Hence, proved.

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