z1 and z2 are two complex numbers such that z1=z2=1. If A=z1¯ −z2z2¯ z1 and B=z1z2-z¯2z¯1, then A−1B−1=----

A−1B−1=BA−1=2 00 2−1=120012

z1 and z2 are two complex numbers such that z1=z2=1. If A=z1¯ −z2z2¯ z1 and B=z1z2-z¯2z¯1, then A−1B−1=----

A−1B−1=BA−1=2 00 2−1=120012

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$z_{1}$ and $z_{2}$ are two complex numbers such that $|z_{1}| = |z_{2}| = 1.$ If $A = [\begin{matrix} \bar{z_{1}} & - z_{2} \\ \bar{z_{2}} & z_{1} \end{matrix}]$ and $B = [\begin{matrix} z_{1} & z_{2} \\ - {\bar{z}}_{2} & {\bar{z}}_{1} \end{matrix}]$ , then $A^{- 1}$ $B^{- 1}$ =----

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$[\begin{array}{l} z_{1} z_{2} \\ \bar{z_{1}} \bar{z_{2}} \end{array}]$

$[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

$[\begin{matrix} \frac{1}{2} & 0 \\ 0 & \frac{1}{2} \end{matrix}]$

$[\begin{array}{l} 2 0 \\ 0 2 \end{array}]$

answer is C.

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$A^{- 1} B^{- 1} = {(B A)}^{- 1} = {(\begin{array}{l} 2 0 \\ 0 2 \end{array})}^{- 1} = [\begin{matrix} \frac{1}{2} & 0 \\ 0 & \frac{1}{2} \end{matrix}]$

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z1 and z2 are two complex numbers such that z1=z2=1. If A=z1¯ −z2z2¯ z1 and B=z1z2-z¯2z¯1, then A−1B−1=----

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$z_{1}$ and $z_{2}$ are two complex numbers such that $|z_{1}| = |z_{2}| = 1.$ If $A = [\begin{matrix} \bar{z_{1}} & - z_{2} \\ \bar{z_{2}} & z_{1} \end{matrix}]$ and $B = [\begin{matrix} z_{1} & z_{2} \\ - {\bar{z}}_{2} & {\bar{z}}_{1} \end{matrix}]$ , then $A^{- 1}$ $B^{- 1}$ =----