# IPMAT Question Paper 2019 | IPM Indore Quants

###### IPMAT Sample Paper | IPMAT Question Paper | Question 4

IPMAT 2019 Question Paper IPM Indore Quantitative Ability. Solve questions from IPMAT 2019 Question Paper from IPM Indore and check the solutions to get adequate practice. The best way to ace IPMAT is by solving IPMAT Question Paper. To solve other IPMAT Sample papers, go here: IPM Sample Paper

Question 4 : Let A, B, C be three 4 X 4 matrices such that det A = 5, det B = -3, and det C = $$frac{1}{2}\\$. Then the det$2AB-1C3BT) is

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Let us recall a few properties of determinants.

det(kA) = kn det(A), where A is a Square Matrix
n is the order of the Square Matrix
k is some scalar constant
det(AB) = det(A) * det(B), where A,B are two matrices compatible for multiplication.
det(A-1)=$$frac{1}{det$A$}$ where A-1 is the inverse of matrix A. det$AT)= det(A) where AT is the transpose of matrix A.

Using the above properties,
det(2AB-1C3BT) = det(2A) * det(B-1) * det(C3) * det(BT)
= 24 det(A) * $$frac{1}{det$B$}$ * det$C) * det(C) * det(C) * det(B)
= 16 * 5 * $$frac{1}{-3}\\$ * $\frac{1}{2}\\$ * $\frac{1}{2}\\$ * $\frac{1}{2}\\$ * -3 = 10. The question is "Let A, B, C be three 4 X 4 matrices such that det A = 5, det B = -3, and det C = $\frac{1}{2}\\$. Then the det$2AB-1C3BT) is"

##### Hence, the answer is 10

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