Which of the following is true for matrices?Question 1Select one:ย (๐ด๐)ย =ย ๐ดย (๐ด๐ต)-1ย =ย ๐ต-1๐ด-1ย ๐ด*๐ผย =ย ๐ด๐ด๐ต=๐ต๐ด
Question
Which of the following is true for matrices?Question 1Select one:ย (๐ด๐)ย =ย ๐ดย (๐ด๐ต)-1ย =ย ๐ต-1๐ด-1ย ๐ด*๐ผย =ย ๐ด๐ด๐ต=๐ต๐ด
Solution
The correct answer is ๐ด*๐ผ = ๐ด.
Here's why:
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(๐ด๐) = ๐ด: This is not always true. The transpose of a matrix ๐ด (denoted ๐ด๐) is a new matrix whose rows are the columns of the original matrix. Unless ๐ด is a symmetric matrix (i.e., ๐ด = ๐ด๐), this statement is false.
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(๐ด๐ต)-1 = ๐ต-1๐ด-1: This is not true. The inverse of a product of two matrices ๐ด and ๐ต (denoted (๐ด๐ต)-1) is equal to the product of the inverses of ๐ต and ๐ด, in that order. So, (๐ด๐ต)-1 = ๐ต-1๐ด-1 is false.
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๐ด*๐ผ = ๐ด: This is true. When a matrix ๐ด is multiplied by the identity matrix ๐ผ (of the same size as ๐ด), the result is ๐ด. This is because the identity matrix acts like the number 1 in real
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