Advertisements
Advertisements
प्रश्न
If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 –7A is equal to ______.
विकल्प
A
I – A
I + A
3A
Advertisements
उत्तर
If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 –7A is equal to A.
Explanation:
(A – I)3 + (A + I)3 – 7A = A3 – I3 – 3A2I + 3AI2 + A3 + I3 + 3A2I + 3AI2 – 7A
= 2A3 + 6AI2 – 7A
= 2A.A2 + 6AI – 7A
= 2AI + 6AI – 7A .....[A2 = I]
= 8AI – 7A
= 8A – 7A
= A
APPEARS IN
संबंधित प्रश्न
If \[\begin{pmatrix}a + 4 & 3b \\ 8 & - 6\end{pmatrix} = \begin{pmatrix}2a + 2 & b + 2 \\ 8 & a - 8b\end{pmatrix},\] ,write the value of a − 2b.
If A is square matrix such that A2 = A, show that (I + A)3 = 7A + I..
Matrix addition is associative as well as commutative.
Matrix multiplication is commutative.
If A and B are two square matrices of the same order, then A + B = B + A.
(AB)–1 = A–1. B–1, where A and B are invertible matrices satisfying commutative property with respect to multiplication.
If `"A" = [("a","b"),("b","a")]` and `"A"^2 = [(alpha,beta),(beta, alpha)]` then ____________.
If matrix A `= [("a","b","c"),("b","c","a"),("c","a","b")]` where a, b, c are real positive numbers, abc = 1 and ATA = I, then the value of a3 + b3 + c3 is ____________.
Find the values of x, y, z respectively if the matrix A `= [(0,2"y","z"),("x","y","-z"),("x","-y","z")]` satisfy the equation ATA = I3.
If matrices A and B are inverse of each other then ____________.
If A `= [(5, "x"),("y", 0)]` and A = A' then ____________.
Let \[A=[a_{ij}]\] and \[B=[b_{ij}]\] be two matrices of the same order \[m\times n\]. If \[C=A+B=[c_{ij}]\], which entry rule defines \[C\]?
For matrices \[A=[a_{ij}]\] and \[B=[b_{ij}]\] of the same order \[m\times n\], what is the order of \[C=A+B\]?
Let \[A=[a_{ij}]\] and \[B=[b_{ij}]\] be matrices of the same order \[m\times n\]. If \[D=A-B=[d_{ij}]\], which rule defines \[D\]?
When can matrices be added or subtracted?
Which equation states the commutative property of matrix addition?
Which equation states the associative property of matrix addition?
Which equation expresses the additive identity property for a matrix \[A\]?
Which equation expresses the additive inverse property for a matrix \[A\]?
Given \[A=\begin{bmatrix}\sqrt{3}&1&-1\\2&3&0\end{bmatrix}\] and \[B=\begin{bmatrix}2&\sqrt{5}&1\\-2&3&\frac{1}{2}\end{bmatrix}\], find \[A+B\].
For \[A=\begin{bmatrix}1&2&3\\2&3&1\end{bmatrix}\] and \[B=\begin{bmatrix}3&-1&3\\-1&0&2\end{bmatrix}\], which matrix is \[-B\]?
If \[A=\begin{bmatrix}1&2&3\\2&3&1\end{bmatrix}\] and \[B=\begin{bmatrix}3&-1&3\\-1&0&2\end{bmatrix}\], find \[2A-B\].
Which statement correctly uses the zero matrix \[O\] as the additive identity?
