Let A, B be two matrices such that they commute, then for any positive integer \( n \),
P
(i) \(... VIDEO
Let A, B be two matrices such that they commute, then for any positive integer \( n \),
P
(i) \( \mathrm{AB}^{\mathrm{n}}=\mathrm{B}^{\mathrm{n}} \mathrm{A} \)
W
(ii) \( (\mathrm{AB})^{\mathrm{n}}=\mathrm{A}^{\mathrm{n}} \mathrm{B}^{\mathrm{n}} \)
(1) only (i) is correct
(2) Both (i) and (ii) are correct
(3) only (ii) is correct
(4) none of (i) and (ii) is correct
π²PW App Link - https://bit.ly/YTAI_PWAP
πPW Website - https://www.pw.live
Other Videos By PW Solutions 2023-02-14 For what value of \( \mathrm{x} \), is the matrix \( A=\left[\begin{array}{ccc}0 & 1 & -2 \\ -1 ... 2023-02-14 Directions : Each of these questions contain two statements, Assert... 2023-02-14 Directions : Each of these questions contain two statements, Assert... 2023-02-14 A committee consists of 9 experts taken from three institutions \( ... 2023-02-14 In early earth, water and carbon dioxide was produced by the
\( \ma... 2023-02-14 Directions : Each of these questions contain two statements, Assert... 2023-02-14 Oparin and Haldane believes that life on earth originated by
P
a. S... 2023-02-14 Directions : Each of these questions contain two statements, Assert... 2023-02-14 Column-I
Column-II
(A) In a triangle \( \triangle X Y Z \), let a, b and \( c \) be the lengths ... 2023-02-14 If \( \mathrm{A} \) is a skew - symmetric matrix and \( \mathrm{n} \) is an even positive intege... 2023-02-14 Let A, B be two matrices such that they commute, then for any positive integer \( n \),
P
(i) \(... 2023-02-14 Three ordinary and fair dice are rolled simultaneously. The probabi... 2023-02-14 The reagents used for softening of the temporary hardness of water is/are
(A) \( \mathrm{Ca}_{3}... 2023-02-14 Chemical theory for origin of life was given by
a. Stanley Miller
b... 2023-02-14 Three numbers are selected simultaneously from the set \( \{1,2,3, ... 2023-02-14 Directions : Each of these questions contain two statements, Assert... 2023-02-14 Column I
Column II
(A) Bernoullis theorem
(1) Narrower pipes have l... 2023-02-14 Directions : Each of these questions contain two statements, Assert... 2023-02-14 Column I
Column II
(A) Magnus effect
(1) Pascal's law
(B) Loss of e... 2023-02-14 Organic compounds evolved on earth and required for origin
P of lif... 2023-02-14 Column I
Column II
(A) Water proofing agents
(1) Increase in termin...