A and B are two given matrices such that order of A is 3×4 , if A’ B and BA’ are b

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3 and 4 .Determinants and Matrices

medium

$A$ and $B$ are two given matrices such that the order of $A$ is $3×4$ , if $A’ B$ and $BA’$ are both defined then

order of $B’$ is $3 × 4$

order of $B’A$ is $4 × 4$

order of $B’A$ is $3 × 3$

$B’A$ is undefined

Solution

$A = 3 × 4 ; A’ = 4×3$
As $A’ B$ is defined ==> let order of $B = 3 × n$
now $BA’ = (3 ×n) × (4 × 3) ==> n = 4$
$\therefore$ order of $B is 3 × 4$
$\therefore$ order of $B’ = 4 × 3$
order of $B’ A = (4×3) × (3 × 4) = 4 × 4$

Standard 12

Mathematics

If $A$ is a skew symmetric matrix and $n $ is a positive integer, then ${A^n}$ is

normal

If $\mathrm{A}^{\prime}=\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ccc}-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right],$ then verify that $(\mathrm{A}+\mathrm{B})^{\prime}=\mathrm{A}^{\prime}+\mathrm{B}^{\prime}$

medium

Let $A\, = \,\left( {\begin{array}{*{20}{c}}
0&{2q}&r\\
p&q&{ – r}\\
p&{ – q}&r
\end{array}} \right)$. If $A{A^T}\, = \,{I_3},\,\left| p \right|$ then $\left| p \right|$ is

hard

(JEE MAIN-2019)

Let $ A$ be a skew- symmetric matrix of odd order, then $ |A| $ is equal to

normal

Given $A =$$\left[ {\begin{array}{{20}{c}}1&3\\2&2\end{array}} \right]$ ; $I =$$\left[ {\begin{array}{{20}{c}}1&0\\0&1\end{array}} \right]$ . $If A – \lambda I$ is a singular matrix then

normal

$A$ and $B$ are two given matrices such that the order of $A$ is $3×4$ , if $A’ B$ and $BA’$ are both defined then

Solution

Similar Questions

If $A$ is a skew symmetric matrix and $n $ is a positive integer, then ${A^n}$ is

If $\mathrm{A}^{\prime}=\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ccc}-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right],$ then verify that $(\mathrm{A}+\mathrm{B})^{\prime}=\mathrm{A}^{\prime}+\mathrm{B}^{\prime}$

Let $A\, = \,\left( {\begin{array}{*{20}{c}} 0&{2q}&r\\ p&q&{ – r}\\ p&{ – q}&r \end{array}} \right)$. If $A{A^T}\, = \,{I_3},\,\left| p \right|$ then $\left| p \right|$ is

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Given $A =$$\left[ {\begin{array}{*{20}{c}}1&3\\2&2\end{array}} \right]$ ; $I =$$\left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$ . $If A – \lambda I$ is a singular matrix then

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Let $A\, = \,\left( {\begin{array}{*{20}{c}}
0&{2q}&r\\
p&q&{ – r}\\
p&{ – q}&r
\end{array}} \right)$. If $A{A^T}\, = \,{I_3},\,\left| p \right|$ then $\left| p \right|$ is

Given $A =$$\left[ {\begin{array}{{20}{c}}1&3\\2&2\end{array}} \right]$ ; $I =$$\left[ {\begin{array}{{20}{c}}1&0\\0&1\end{array}} \right]$ . $If A – \lambda I$ is a singular matrix then