If A=05−4a04bb2−5b0 is a skew symmetric matrix, then a+b=_____

$$A=05$$−$$4a04bb2$$−$$5b0$$ is skewSymmetric matrix.So,aij−$$ajia=$$−$$5$$,$$b=4a+b=$$−$$1$$

Q.

If $A = [\begin{matrix} 0 & 5 & - 4 \\ a & 0 & 4 \\ b & b^{2} - 5 b & 0 \end{matrix}]$ is a skew symmetric matrix, then $a + b =_____$

Moderate

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answer is C.

(Detailed Solution Below)

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Detailed Solution

$A = [\begin{matrix} 0 & 5 & - 4 \\ a & 0 & 4 \\ b & b^{2} - 5 b & 0 \end{matrix}]$ is skew

Symmetric matrix.

So,

$a_{i j} - a_{j i}$

$a = - 5, b = 4$

$a + b = - 1$

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