The product [ a b - b a ] [ a - b b a ] is equal to:

Question

The product $[\begin{matrix} a & b \\ - b & a \end{matrix}] [\begin{matrix} a & - b \\ b & a \end{matrix}]$ is equal to:

Smart Achievers · Accepted Answer

(1)

Ans. $[\begin{matrix} a^{2} + b^{2} & 0 \\ 0 & a^{2} + b^{2} \end{matrix}]$

Explanation:

$[\begin{matrix} a & b \\ - b & a \end{matrix}] [\begin{matrix} a & - b \\ b & a \end{matrix}] = [\begin{matrix} a^{2} + b^{2} & - a b + b a \\ - b a + a b & b^{2} + a^{2} \end{matrix}]$

$= [\begin{matrix} a^{2} + b^{2} & 0 \\ 0 & a^{2} + b^{2} \end{matrix}]$

Solution

Q.
The product $[\begin{matrix} a & b \\ - b & a \end{matrix}] [\begin{matrix} a & - b \\ b & a \end{matrix}]$ is equal to:

1 $[\begin{matrix} a^{2} + b^{2} & 0 \\ 0 & a^{2} + b^{2} \end{matrix}]$

2 $[\begin{matrix} {(a + b)}^{2} & 0 \\ {(a + b)}^{2} & 0 \end{matrix}]$

3 $[\begin{matrix} a^{2} + b^{2} & 0 \\ a^{2} + b^{2} & 0 \end{matrix}]$

4 $[\begin{matrix} a & 0 \\ 0 & b \end{matrix}]$

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Solution

Q. The product [ab-ba][a-bba] is equal to:

1 [a2+b200a2+b2]

2 [(a+b)20(a+b)20]

3 [a2+b20a2+b20]

4 [a00b]