If $$A=1-12-1$$ ,$$B=a1b-1$$ and $$A+B2=A2+B2$$ , the value of a $$+$$ b is

$$A+B2=A2+B2$$⇒$$AB+BA=0$$ ⇒$$1-12-1a1b-1+a1b-11-12-1=0$$ ⇒$$a-b22a-b3+a+2-a-1b-2-b+1=0$$⇒$$a=1$$,$$b=4$$⇒$$a+b=5$$

Operations of matrix

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If $A = [\begin{matrix} 1 & - 1 \\ 2 & - 1 \end{matrix}]$ , $B = [\begin{matrix} a & 1 \\ b & - 1 \end{matrix}]$ and ${(A + B)}^{2} = A^{2} + B^{2}$ , the value of a + b is

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Solution

${(A + B)}^{2} = A^{2} + B^{2} \Rightarrow A B + B A = 0 \Rightarrow [\begin{matrix} 1 & - 1 \\ 2 & - 1 \end{matrix}] [\begin{matrix} a & 1 \\ b & - 1 \end{matrix}] + [\begin{matrix} a & 1 \\ b & - 1 \end{matrix}] [\begin{matrix} 1 & - 1 \\ 2 & - 1 \end{matrix}] = 0 \Rightarrow [\begin{matrix} a - b & 2 \\ 2 a - b & 3 \end{matrix}] + [\begin{matrix} a + 2 & - a - 1 \\ b - 2 & - b + 1 \end{matrix}] = 0 \Rightarrow a = 1, b = 4 \Rightarrow a + b = 5$

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Operations of matrix

Remember concepts with our Masterclasses.

If A=1-12-1 ,B=a1b-1 and A+B2=A2+B2 , the value of a + b is

A+B2=A2+B2⇒AB+BA=0 ⇒1-12-1a1b-1+a1b-11-12-1=0 ⇒a-b22a-b3+a+2-a-1b-2-b+1=0⇒a=1,b=4⇒a+b=5

Ready to Test Your Skills?

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If $A = [\begin{matrix} 1 & - 1 \\ 2 & - 1 \end{matrix}]$ , $B = [\begin{matrix} a & 1 \\ b & - 1 \end{matrix}]$ and ${(A + B)}^{2} = A^{2} + B^{2}$ , the value of a + b is