1.

If A = \(\begin{bmatrix}ab & b^2 \\[0.3em]-a^2 & -ab \\[0.3em]\end{bmatrix}\), show that A2 = 0

Answer»

Given,

A = \(\begin{bmatrix} ab & b^2 \\[0.3em] -a^2 & -ab \\[0.3em] \end{bmatrix}\)

A2 \(\begin{bmatrix} ab & b^2 \\[0.3em] -a^2 & -ab \\[0.3em] \end{bmatrix}\)\(\begin{bmatrix} ab & b^2 \\[0.3em] -a^2 & -ab \\[0.3em] \end{bmatrix}\)

\(\begin{bmatrix} a^2b^2-a^2b^2 & ab^3-ab^3 \\[0.3em] -a^3b+a^3b & -a^2b^2+a^2b^2 \\[0.3em] \end{bmatrix}\) 

\(\begin{bmatrix} 0 &0 \\[0.3em] 0 & 0 \\[0.3em] \end{bmatrix}\) 

= 0

Hence,

A2 = 0



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