Class 12Mathematics3-4. Matrices and DeterminantsSpecial types of matrices, Transpose of matrices and Trace of matrices
MediumIf $A$ and $B$ are square matrices of the same order,then which of the following properties holds true for the transpose of their product?
- A$(AB)' = A'B'$
- B$(AB)' = B'A'$
- C$AB = O$ if $|A| = 0$ or $|B| = 0$
- D$AB = O$ if $A = I$ or $B = I$
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Express the following matrix as the sum of a symmetric and a skew-symmetric matrix: $\left[\begin{array}{rrr}6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3\end{array}\right]$
Medium
View SolutionIf $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $A + A^{\prime} = I$,then the value of $\alpha$ is . . . . . . .
Which of the following relations regarding the transpose of a matrix is incorrect?
Easy
View SolutionIf $A$ is a skew-symmetric matrix,then (given $n \in N$):
$1$. $A^{2n}$ is a skew-symmetric matrix.
$2$. $A^{2n+1}$ is a skew-symmetric matrix.
$1$. $A^{2n}$ is a skew-symmetric matrix.
$2$. $A^{2n+1}$ is a skew-symmetric matrix.
If $A$ and $B$ are square matrices of the same order and $B$ is a skew-symmetric matrix,then $A^{\prime} B A$ is
MediumKCET 2020
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