First slide

Operations of matrix

Question

If $A = [\begin{array}{cc} a b & b^{2} \\ - a^{2} & - a b \end{array}]$ , then A² is equal

Easy

A

$O$
B

$I$
C

$- I$
D

none of these

Solution

$\begin{aligned} A^{2} = [\begin{array}{cc} a b & b^{2} \\ - a^{2} & - a b \end{array}] [\begin{array}{cc} a b & b^{2} \\ - a^{2} & - a b \end{array}] \\ = [\begin{array}{cc} a^{2} b^{2} - a^{2} b^{2} & a b^{3} - a b^{3} \\ - a^{3} b + a^{3} b & - a^{2} b^{2} + a^{2} b^{2} \end{array}] = O \end{aligned}$

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