Choose the correct statement related to the matrices A- 1 0- 0 1 - and B- 0 1- 1 0 -

The correct option is C A^3=A, B^3 = B Clearly, A is an identity matrix #160;Now, A ^ 3 = #160; [ 1 amp; 0; 0 amp; 1 ][ ...

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Standard XII

Mathematics

Addition and Subtraction of a Matrix

Choose the co...

Question

Choose the correct statement related to the matrices $A = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}]$ and $B = [\begin{matrix} 0 & 1 1 & 0 \end{matrix}]$

A^{3} = A, B^{3} \neq B

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A^{3} \neq A, B^{3} = B

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A^{3} = A, B^{3} = B

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A^{3} \neq A, B^{3} \neq B

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Solution

The correct option is C $A^{3} = A, B^{3} = B$
Clearly, $A$ is an identity matrix

Now, $A^{3} =$ $[\begin{matrix} 1 & 0 0 & 1 \end{matrix}] [\begin{matrix} 1 & 0 0 & 1 \end{matrix}] [\begin{matrix} 1 & 0 0 & 1 \end{matrix}]$

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

$⟹ A^{3} = A$

Also, $B^{3} = [\begin{matrix} 0 & 1 1 & 0 \end{matrix}] [\begin{matrix} 0 & 1 1 & 0 \end{matrix}] [\begin{matrix} 0 & 1 1 & 0 \end{matrix}] = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}] [\begin{matrix} 0 & 1 1 & 0 \end{matrix}] = [\begin{matrix} 0 & 1 1 & 0 \end{matrix}] = B$

$⟹ B^{3} = B$

Hence, option C is correct.

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Choose the correct statement related to the matrices A=[1001] and B=[0110]

The correct option is C A3=A,B3=BClearly, A is an identity matrix Now, A3= [1001][1001][1001] =[1001][1001]=[1001]=A⟹A3=AAlso, B3=[0110][0110][0110]=[1001][0110]=[0110]=B⟹B3=BHence, option C is correct.

Choose the correct statement related to the matrices $A = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}]$ and $B = [\begin{matrix} 0 & 1 1 & 0 \end{matrix}]$