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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Three

${(A B)}^{- 1} = A^{- 1} B^{- 1}$ , where $A$ and $B$ are invertible matrices satisfying the commutative property with respect to multiplication.

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Payal Gupta | Contributor-Level 10

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T r u e . \\ I f A a n d B a r e i n v e r t i b l e m a t r i c e s o f t h e s a m e o r d e r . \\ ∴ {(A B)}^{- 1} = {(B A)}^{- 1} [? A B = B A] \\ B u t {(A B)}^{- 1} = A^{- 1} B^{- 1} [G i v e n] \\ ∴ {(B A)}^{- 1} = B^{- 1} A^{- 1} \\ A^{- 1} B^{- 1} = B^{- 1} A^{- 1} \\ ∴ A a n d B s a t i s f y c o m m u t a t i v e p r o p e r t y w . r . t m u l t i p l i c a t i o n . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Three

If $A$ is a skew symmetric matrix, then $A^{2}$ is a symmetric matrix.

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Payal Gupta | Contributor-Level 10

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T r u e . \\ {(A^{2})}^{'} = {(A^{'})}^{2} \\ = {[- A]}^{2} [? A^{'} = - A] \\ = A^{2} \\ S o, A^{2} i s a s y m m e t r i c m a t r i x . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Three

If then $A B$ and $B A$ are defined and equal.

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Payal Gupta | Contributor-Level 10

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Three

$A A^{'}$ is always a symmetric matrix for any matrix $A$ .

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Payal Gupta | Contributor-Level 10

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T r u e . \\ L e t P = A A^{'} \\ P^{'} = {(A A^{'})}^{'} \\ = {(A^{'})}^{'} . A^{'} [? {(A B)}^{'} = B^{'} A^{'}] \\ = A A^{'} = P \\ S o, P i s a s y m m e t r i c m a t r i x . \\ H e n c e, A A^{'} i s a l w a y s a s y m m e t r i c m a t r i x . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Three

If $A$ , $B$ , and $C$ are square matrices of the same order, then $A B = A C$ always implies that $B = C$ .

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Payal Gupta | Contributor-Level 10

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} F a l s e . \\ A = [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}], B = [\begin{matrix} 0 & 0 \\ 2 & 0 \end{matrix}] a n d C = [\begin{matrix} 0 & 0 \\ 3 & 4 \end{matrix}] \\ ∴ A B = [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}] [\begin{matrix} 0 & 0 \\ 2 & 0 \end{matrix}] = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] \\ ∴ A C = [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}] [\begin{matrix} 0 & 0 \\ 3 & 4 \end{matrix}] = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] \\ H e r e A B = A C = 0 b u t B \neq C . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Three

If ${(A B)}^{'} = B^{'} A^{'}$ , where $A$ and $B$ are not square matrices, then the number of rows in $A$ is equal to the number of columns in $B$ and the number of columns in $A$ is equal to the number of rows in $B$ .

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Payal Gupta | Contributor-Level 10

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T r u e . \\ L e t A = {[a_{i j}]}_{m \times n} a n d B = {[b_{i j}]}_{p \times q} \\ A B i s d e f i n e d w h e n n = P \\ ∴ O r d e r o f A B = m \times q \\ \Rightarrow O r d e r o f {(A B)}^{'} = q \times m \\ O r d e r o f B^{'} i s q \times p a n d o r d e r o f A^{'} i s n \times m \\ ∴ B^{'} A^{'} i s d e f i n e d w h e n P = n \\ a n d t h e o r d e r o f B^{'} A^{'} i s q \times m \\ H e n c e, O r d e r o f {(A B)}^{'} = O r d e r o f B^{'} A^{'} i . e ., q \times m . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Three

If $A$ and $B$ are any two matrices of the same order, then ${(A B)}^{'} = A^{'} B^{'}$ .

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Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} F a l s e . \\ Since {(A B)}^{'} = B^{'} A^{'} . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Three

If each of the three matrices of the same order is symmetric, then their sum is a symmetric matrix.

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Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T r u e . \\ L e t A, B, a n d C b e t h r e e m a t r i c e s o f t h e s a m e o r d e r . \\ G i v e n t h a t A^{'} = A, B^{'} = B, a n d C^{'} = C \\ L e t P = A + B + C \\ \Rightarrow P^{'} = {(A + B + C)}^{'} \\ = A^{'} + B^{'} + C^{'} = A + B + C = P \\ S o, A + B + C i s a l s o a s y m m e t r i c m a t r i x . \end{array}$