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In this lesson, we will learn how to use the matrix multiplication to determine the square and cube of a square matrix.

Q1:

Which of the following represents a matrix such that , yet and ?

Q2:

Consider the matrix

Find π΄ 2 .

Find π΄ 3 .

Q3:

Consider What is π β π ο¨ ο¨ ?

Q4:

Which of the following statements is true for all π Γ π matrices π΄ and π΅ ?

Q5:

For write π΄ 2 as a multiple of π΄ .

Q6:

Find β β β β 3 2 1 β 1 2 0 β β β β 3 5 and l i m π β β π β β β β 3 2 1 β 1 2 0 β β β β .

Q7:

Given that π is a 3 Γ 3 zero matrix, find π π‘ .

Q8:

Q9:

Given that the eigenvalues of the nondefective π Γ π matrix π΄ are 1 and β 1 , find π΄ 1 2 .

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