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A =  and B = , find (AB)T

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Option 2 :
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Detailed Solution

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Concept:

Transpose of a Matrix:

The new matrix obtained by interchanging the rows and columns of the original matrix is called as the transpose of the matrix.

It is denoted by A′ or AT

Calculation:

Given A =  and B = 

AB =  × 

AB = 

AB = 

∴ (AB)T = 

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More Transpose of a Matrix Questions

Q1.If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C = A + B?
Q2.If (AB + B)T = BTX  then X is equal to ?
Q3.If \(A - 2I = \begin{bmatrix} -1 & -2 & 3 \\\ 2 & 1 & -1 \\\ -3 & 1 & 0 \end{bmatrix}\) then find AAT where I is the identity matrix of order 3 × 3.
Q4.A = \(\begin{bmatrix} 1& -1 &0 \\ 3& 2 & -1 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 \\ 3\\ 5 \end{bmatrix}\), find (AB)T
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Q6.If \(A = \left[ {\begin{array}{*{20}{c}} {\cos 2θ }&{ - \sin 2θ }\\ {\sin 2θ }&{\cos 2θ } \end{array}} \right]\) and A + AT = I Where I is the unit matrix of 2 × 2 & AT is the transpose of A, then the value of θ is equal to ?
Q7.If A, B are square matrices of the same order and B is a skew-symmetric matrix, then A′BA is:
Q8.If A and B are square matrices of the same order, then (AB′ - BA′) is a:
Q9.If A is a square matrix, then A - A' is a:

More Matrices Questions

Q1.What is A-1 equal to?  
Q2.What is A(adj A) equal to?  
Q3.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? 
Q4.Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct? 
Q5.Let X be a matrix of order 3 x 3, Y be a matrix of order 2 x 3 and Z be a matrix of order 3 × 2. Which of the following statements are correct? I. (ZY)X is defined and is a square matrix of order 3. II. Y(XZ) is defined and is a square matrix of order 2. III. X(YZ) is not defined. Select the answer using the code given below.
Q6.If \(A=\left[\begin{array}{cc} 1 & 3 \\ 0 & -1 \end{array}\right]\), then trace of 5A5 + 4A4 + 3A3 + 2A2 + A + I2 is :
Q7.Let α be a root of the equation x2 + x+ 1= 0 and the matrix A = \(\frac{1}{\sqrt{3}}\left[\begin{array}{ccc} 1 & 1 & 1 \\ 1 & \alpha & \alpha^2 \\ 1 & \alpha^2 & \alpha^4 \end{array}\right]\) then the matrix A31 is equal to
Q8.Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A2B2 − B2A2)X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has:
Q9.Let α ∈ (0, α) and \(A = \begin{bmatrix} 1 & 2 & \alpha \\\ 1 & 0 & 1 \\\ 0 & 1 & 2 \end{bmatrix}\). If det(adj(2A - AT). adj(A - 2AT)) = 28, then (det(A))2 is equal to: 
Q10.For a 3 × 3 matrix A = [aij], whose element aij is given by aij = \(\rm \sqrt{i^2+3j}\) then what is element a31?
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