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Find a matrix X such that 2A + B + X = 0 , where

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Concept:

Two matrices may be added or subtracted only if they have the same dimension; that is, they must have the same number of rows and columns. 

Addition or subtraction is accomplished by adding or subtracting corresponding elements.

 

Calculations:

Given, 

Consider, 2A + B + X = 0

⇒  + X = 

Two matrices may be added or subtracted only if they have the same dimension; that is, they must have the same number of rows and columns. Addition or subtraction is accomplished by adding or subtracting corresponding elements.

⇒  + X = 

⇒ X =  - 

⇒ X = 

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Q1.Consider the following in respect of the matrices  \(\rm P=\begin{bmatrix}0&c&-b\\\ -c&0&a\\\ b&-a&0\end{bmatrix}\ and\ \rm Q=\begin{bmatrix}a^2&ab&ac\\\ ab&b^2&bc\\\ ac&bc&c^2\end{bmatrix}\) I. PQ is a null matrix.  II. QP is an identity matrix of order 3.  III. PQ = QP Which of the above is/are correct? 
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Q2.What is A(adj A) equal to?  
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